On generating properties of the weak commutativity of p -groups, p odd
Year: 2025
Type: article
Abstract: In the present paper, we examine the generating properties of Sidki’s weak commutativity group. More precisely, if G and G φ {G^{\varphi}} are two isomorphic groups, the weak commutativity group χ ( G ) {\chi(G)} is the group generated by G and G φ {G^{\varphi}} subject to the relations [ g , g φ ] = 1 {[g,g^{\varphi}]=1} for all g ∈ G {g\in G} . Here we provide bounds for the number of generators of some subgroups of χ ( G ) {\chi(G)} when G is a p -group of odd order and either G is powerful or D ( G ) {D(G)} is abelian.
Source: Georgian Mathematical Journal
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W4408078434