In the present paper, we examine the generating properties of Sidki's weak commutativity group. More precisely, if G and G phi are two isomorphic groups, the weak commutativity group chi ( G ) is the group generated by G and G phi subject to the relations [ g , g phi ] = 1 for all g is an element of G. Here we provide bounds for the number of generators of some subgroups of chi ( G ) when G is a p-group of odd order and either G is powerful or D ( G ) is abelian.
On generating properties of the weak commutativity of p-groups, p odd
Monetta C.
2025
Abstract
In the present paper, we examine the generating properties of Sidki's weak commutativity group. More precisely, if G and G phi are two isomorphic groups, the weak commutativity group chi ( G ) is the group generated by G and G phi subject to the relations [ g , g phi ] = 1 for all g is an element of G. Here we provide bounds for the number of generators of some subgroups of chi ( G ) when G is a p-group of odd order and either G is powerful or D ( G ) is abelian.File in questo prodotto:
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