TY - JOUR
T1 - Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
AU - Parker, Chris
AU - Saunders, Jack
N1 - Not yet published as of 23/04/2024.
PY - 2023/6/8
Y1 - 2023/6/8
N2 - For p a prime, G a finite group and A a normal subset of elements of order p, we prove that if A2={ab ∣ a,b ∈ A} consists of p-elements then Q=⟨A⟩ is soluble. Further, if Op(G)=1, we show that p is odd, F(Q) is a non-trivial p′-group and Q/F(Q) is an elementary abelian p-group. We also provide examples which show this conclusion is best possible.
AB - For p a prime, G a finite group and A a normal subset of elements of order p, we prove that if A2={ab ∣ a,b ∈ A} consists of p-elements then Q=⟨A⟩ is soluble. Further, if Op(G)=1, we show that p is odd, F(Q) is a non-trivial p′-group and Q/F(Q) is an elementary abelian p-group. We also provide examples which show this conclusion is best possible.
UR - https://www.springer.com/journal/11856
M3 - Article
SN - 0021-2172
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -