Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem

Christopher Parker; Jack Saunders

doi:10.1007/s11856-024-2706-x

Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem

Christopher Parker^*, Jack Saunders

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

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.

Original language	English
Number of pages	20
Journal	Israel Journal of Mathematics
Early online date	18 Dec 2024
DOIs	https://doi.org/10.1007/s11856-024-2706-x
Publication status	E-pub ahead of print - 18 Dec 2024

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title = "Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem",

abstract = "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.",

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AU - Saunders, Jack

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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.

U2 - 10.1007/s11856-024-2706-x

DO - 10.1007/s11856-024-2706-x

M3 - Article (Academic Journal)

SN - 0021-2172

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem

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