Year: 2024
Type: article
Abstract: For p a prime, G a finite group and A a normal subset of elements of order p, we prove that if A 2 = {ab ∣ a,b ∈ A} consists of p-elements then Q = 〈A〉 is soluble. Further, if O p (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.
Source: Israel Journal of Mathematics
Authors: Chris Parker, Jack Saunders
Institutions: University of Birmingham, The University of Western Australia
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4405686726