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 30/07/2024.

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 -