Chris Parker

Accepting PhD Students

PhD projects

Chris Parker’s recent research has been focused on theorems designed to understand the classification theorem of the finite simple groups. This includes joint work primarily with Gernot Stroth, which aims to determine the finite simple groups of local characteristic p. Chris also contributes to projects which explore the appearance of exotic fusion systems and their relationship to finite simple groups. Important contributions here are separate joint works with Jason Semeraro and Valentina Grazian.

Research activity per year

83 Article
2 Book
1 Chapter
1 Chapter (peer-reviewed)
More
- 1 Comment/debate
- 1 Working paper

1 - 50 out of 89 results

2024
The global structure theorem for finite groups with an abelian large p-subgroup
Meierfrankenfeld, U., Parker, C. & Stroth, G., 15 Feb 2024, In: Journal of Algebra. 640, p. 174-215 42 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
21 Downloads (Pure)
Vertex stabilizers of locally s-arc transitive graphs of pushing up type
Parker, C. & van Bon, J., 4 Apr 2024, (Accepted/In press) In: Journal of Algebraic Combinatorics.
Research output: Contribution to journal › Article › peer-review

Open Access
2023
Finite groups which are almost groups of Lie type in characteristic p
Parker, C., Pientka, G., Seidel, A. & Stroth, G., 17 Nov 2023, In: Memoirs of the American Mathematical Society. 292, 1452
Research output: Contribution to journal › Article › peer-review

Open Access
File
117 Downloads (Pure)
Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
Parker, C. & Saunders, J., 8 Jun 2023, (Accepted/In press) In: Israel Journal of Mathematics.
Research output: Contribution to journal › Article › peer-review

Open Access
2022
On the P~!-theorem
Parker, C. & Stroth, G., Feb 2022, In: Archiv der Mathematik. 118, 2, p. 123-132 10 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
19 Downloads (Pure)
Saturated fusion systems on p-groups of maximal class
Parker, C. & Grazian, V., 21 Jul 2022, (Accepted/In press) In: Memoirs of the American Mathematical Society.
Research output: Contribution to journal › Article › peer-review

Open Access
File
64 Downloads (Pure)
2021
2-minimal subgroups of orthogonal groups
Parker, C. & Rowley, P., 29 Oct 2021, (E-pub ahead of print) In: Journal of Algebra.
Research output: Contribution to journal › Article › peer-review

Open Access
File
31 Downloads (Pure)
Algorithms for fusion systems with applications to p-groups of small order
Parker, C. & Semeraro, J., 23 Apr 2021, (E-pub ahead of print) In: Mathematics of Computation. 90, 331, p. 2415-2461
Research output: Contribution to journal › Article › peer-review

Open Access
File
180 Downloads (Pure)
Rank one isolated p-minimal subgroups in finite groups
Meierfrankenfeld, U., Parker, C. & Rowley, P., 15 Jan 2021, In: Journal of Algebra. 566, p. 1-93 93 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
162 Downloads (Pure)
The 2-minimal subgroups of symplectic groups
Parker, C. & Rowley, P., Sept 2021, In: Journal of Pure and Applied Algebra. 225, 9, 14 p., 106643.
Research output: Contribution to journal › Article › peer-review

Open Access
File
74 Downloads (Pure)
2020
2-minimal subgroups of monomial, linear and unitary groups
Parker, C. & Rowley, P., 1 Feb 2020, In: Journal of Algebra. 543, p. 1-53 53 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

171 Downloads (Pure)
The Local Structure Theorem, the non-characteristic 2 case
Parker, C. & Stroth, G., 1 Apr 2020, In: London Mathematical Society. Proceedings . 120, 4, p. 465-513
Research output: Contribution to journal › Article › peer-review

Open Access
File
164 Downloads (Pure)
2019
Fusion systems on maximal class 3-groups of rank two revisited
Parker, C. & Semeraro, J., Sept 2019, In: Proceedings of the American Mathematical Society. 147, 9, p. 3773–3786 14 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
231 Downloads (Pure)
Groups St Andrews 2017 in Birmingham
Cambell, C., Parker, C., Quick, M., Robertson, E. & Roney-Dougal, C. M., 11 Apr 2019, London Mathematical Society Lecture Note Series ed. Cambridge University Press. 510 p.
Research output: Book/Report › Book
The local structure theorem: the wreath product case
Parker, C. & Stroth, G., 22 Aug 2019, (E-pub ahead of print) In: Journal of Algebra. 25 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
103 Downloads (Pure)
2018
Fusion systems over a Sylow p-subgroup of G₂(p)
Parker, C. & Semeraro, J., Jun 2018, In: Mathematische Zeitschrift. 289, 1-2, p. 629–662 34 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
3 Citations (Scopus)

153 Downloads (Pure)
2017
Locally ﬁnite groups in which every non-cyclic subgroup is self-centralizing
Delizia, C., Parker, C., Moravec, P., Nicotera, C. & Jezernik, U., Feb 2017, In: Journal of Pure and Applied Algebra. 221, 2, p. 401–410
Research output: Contribution to journal › Article › peer-review

Open Access
File
6 Citations (Scopus)

137 Downloads (Pure)
2016
A 2-local identification of PΩ₈⁺(3)
Parker, C. & Stroth, G., 25 Apr 2016, (E-pub ahead of print) In: Journal of Pure and Applied Algebra. 220, 10, 27 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
149 Downloads (Pure)
2015
A characterisation of almost simple groups with socle ²E₆(2) or M(22)
Parker, C., Stroth, G. & Salarian, R., Sept 2015, In: Forum Math. 27, 5, p. 2853–2899 46 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
167 Downloads (Pure)
A family of fusion systems related to the groups Sp4(pa) and G2(pa)
Parker, C., Apr 2015, In: Archiv der Mathematik. 104, 4, p. 311-323 12 p.
Research output: Contribution to journal › Article › peer-review
3 Citations (Scopus)
Remarks on lifting Beauville structures of quasisimple groups
Magaard, K. & Parker, C., 1 Jan 2015, Beauville Surfaces and Groups. Bauer, I., Garion, S. & Vdovina, A. (eds.). Springer, p. 121-128 8 p. (Springer Proceedings in Mathematics & Statistics).
Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review
What are the C₂-groups?
Capdeboscq, I. & Parker, C., 1 Jan 2015, Groups St Andrews 2013. Cambridge University Press, p. 194-208 15 p.
Research output: Chapter in Book/Report/Conference proceeding › Chapter
2014
An improved 3-local characterization of McL and its automorphism group
Parker, C. & Stroth, G., 15 May 2014, In: Journal of Algebra. 406, p. 69-90
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

147 Downloads (Pure)
Examples of groups with the same number of subgroups of every index
Parker, C. W. & Kanchana, A. A. C., 14 Apr 2014, In: Journal of Siberian Federal University - Mathematics and Physics. 7, 1, p. 95-99 5 p.
Research output: Contribution to journal › Article › peer-review
F₄(2) and its automorphism group
Parker, C. & Stroth, G., May 2014, In: Journal of Algebra. 218, 5, p. 852–878
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

123 Downloads (Pure)
2013

Erratum: Generation of finite quasisimple groups with an application to groups acting on beauville surfaces (Proc. London Math Soc. (2013) 107:3 (744-798)
Fairbairn, B., Magaard, K. & Parker, C., 1 Nov 2013, In: Proceedings of the London Mathematical Society. 107, 5, 1 p.
Research output: Contribution to journal › Comment/debate › peer-review

Open Access

6 Citations (Scopus)
Generation of finite quasisimple groups with an application to groups acting on Beauville surfaces
Parker, C., Magaard, K. & Fairbairn, B., 18 Feb 2013, In: London Mathematical Society. Proceedings . p. 1-55 55 p.
Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)
The commuting graph of a soluble group
Parker, C., 2013, In: Bulletin of the London Mathematical Society.
Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)
The diameter of the commuting graph of a finite group with trivial centre
Morgan, G. L. & Parker, C., 1 Nov 2013, In: Journal of Algebra. 393, p. 41-59
Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)
There is no upper bound for the diameter of the commuting graph of a finite group
Giudici, M. & Parker, C., 1 Sept 2013, In: Journal of Combinatorial Theory. Series A. 120, 7, p. 1600-1603 4 p.
Research output: Contribution to journal › Article › peer-review

Open Access
20 Citations (Scopus)
2012
An identification theorem for groups with socle PSU₆ (2)
Parker, C. & Stroth, G., 1 Dec 2012, In: Journal of the Australian Mathematical Society. 93, 3, p. 277-310 34 p.
Research output: Contribution to journal › Article › peer-review

Open Access
2 Citations (Scopus)
An identification theorem for the sporadic simple groups F_2 and M(23)
Parker, C. & Stroth, G., Dec 2012, In: Journal of Group Theory. 93, 03, p. 277-310
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

211 Downloads (Pure)
A note on groups in which the centralizer of every element of order 5 is a 5-group
Parker, C., Astill, S. & Waldecker, R., 2012, In: Siberian Mathematical Journal.
Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)
On a class of affine geometries
Hoffman, C., Parker, C. W. & Shpectorov, S., 1 Sept 2012, In: Advances in Geometry. 12, 3, p. 381-399 19 p.
Research output: Contribution to journal › Article › peer-review
3 Citations (Scopus)
2011

Completely reducible subcomplexes of spherical buildings
Parker, C. & Tent, K., 1 Aug 2011, In: Archiv der Mathematik. 97, 2, p. 125-128 4 p.
Research output: Contribution to journal › Article

1 Citation (Scopus)
Strongly p-embedded Subgroups
Parker, C. & Stroth, G., 1 Jan 2011, In: Pure and Applied Mathematics Quarterly. 7, 3, p. 797-858 62 p.
Research output: Contribution to journal › Article
6 Citations (Scopus)
2010
A note on conjugacy of supplements in finite soluble groups
Parker, C. & Rowley, P., 1 Jun 2010, In: Bulletin of the London Mathematical Society. 42, p. 417-419 3 p.
Research output: Contribution to journal › Article
5 Citations (Scopus)
Recognising simplicity of black-box groups by constructing involutions and their centralisers
Parker, C. & Wilson, RA., 1 Sept 2010, In: Journal of Algebra. 324, 5, p. 885-915 31 p.
Research output: Contribution to journal › Article
18 Citations (Scopus)
Two families of exotic fusion systems
Clelland, M. & Parker, C., 15 Jan 2010, In: Journal of Algebra. 323, 2, p. 287-304 18 p.
Research output: Contribution to journal › Article
5 Citations (Scopus)
2009
A 3-local characterization of C02
Parker, C. & Rowley, P., 1 Jan 2009, In: Journal of Algebra. 323, 3, p. 601-621
Research output: Contribution to journal › Article
4 Citations (Scopus)
A 3-Local Characterization of M-12 and SL3(3)
Astill, S. & Parker, C., 1 Feb 2009, In: Archiv der Mathematik. 92, 2, p. 99-110 12 p.
Research output: Contribution to journal › Article
1 Citation (Scopus)
On strongly p-embedded subgroups of Lie rank 2
Parker, C. & Stroth, G., 3 Nov 2009, In: Archiv der Mathematik.
Research output: Contribution to journal › Article
2 Citations (Scopus)
2008

(S-3, S-6)-amalgams VII
Lempken, W., Parker, C. & Rowley, P., 1 Jan 2008, In: Rendiconti del Seminario Matematico . 119, p. 97-139 43 p.
Research output: Contribution to journal › Article
A 3-local identification of the alternating group of degree 8, the McLaughlin simple group and their automorphism groups
Parker, C. & Rowley, P., 15 Feb 2008, In: Journal of Algebra. 319, 4, p. 1752-1775 24 p.
Research output: Contribution to journal › Article
3 Citations (Scopus)
Isolated subgroups in finite groups
Meierfrankenfeld, U., Parker, C. & Rowley, P., 5 Dec 2008, In: Journal of the London Mathematical Society. 79, 1, p. 107-128 22 p.
Research output: Contribution to journal › Article
1 Citation (Scopus)
2007

(S-3, S-6)-Amalgams VI
Lempken, W., Parker, C. & Rowley, P., 1 Jan 2007, In: Rendiconti del Seminario Matematico . 118, p. 235-256 22 p.
Research output: Contribution to journal › Article

1 Citation (Scopus)
$(S\sb 3,S\sb 6)$-amalgams. V
Lempken, W., Parker, C. & Rowley, P., 1 Jan 2007, In: Rendiconti del Seminario Matematico . 117, p. 231-256 26 p.
Research output: Contribution to journal › Article
$(S\sb 3,S\sb 6)$-amalgams. VI
Lempken, W., Parker, C. & Rowley, P., 1 Jan 2007, In: Rendiconti del Seminario Matematico . 118, p. 235-256 22 p.
Research output: Contribution to journal › Article
A 3-local characterization of Co3
Korchagina, I., Parker, C. & Rowley, P., 1 Feb 2007, In: European Journal of Combinatorics. 28, 2, p. 559-566 8 p.
Research output: Contribution to journal › Article
1 Citation (Scopus)
2006

$(S\sb 3,S\sb 6)$-amalgams. IV
Lempken, W., Parker, C. & Rowley, P., 1 Jan 2006, In: Universita di Padova Seminario Matematico Rendiconti. 114, p. 1-19 19 p.
Research output: Contribution to journal › Article

Chris Parker

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