Let G be a finite group of odd order admitting an involutory automorphism ϕ, and let G-ϕ be the set of elements of G transformed by ϕ into their inverses. Note that [ G, ϕ] is precisely the subgroup generated by G-ϕ. Suppose that each subgroup generated by a subset of G-ϕ can be generated by at most r elements. We show that the rank of [ G, ϕ] is r-bounded.
On the rank of a finite group of odd order with an involutory automorphism / Acciarri, C; Shumyatsky, P. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - 194:3(2021), pp. 461-469. [10.1007/s00605-020-01479-4]
On the rank of a finite group of odd order with an involutory automorphism
Acciarri C;
2021
Abstract
Let G be a finite group of odd order admitting an involutory automorphism ϕ, and let G-ϕ be the set of elements of G transformed by ϕ into their inverses. Note that [ G, ϕ] is precisely the subgroup generated by G-ϕ. Suppose that each subgroup generated by a subset of G-ϕ can be generated by at most r elements. We show that the rank of [ G, ϕ] is r-bounded.
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