Let G be a finite group and let k≥2 We prove that the coprime subgroup γ*k(G) is nilpotent if and only if |xy|=|x||y| for any γ*k -commutators x,yϵG of coprime orders (Theorem A). Moreover, we show that the coprime subgroup γ*k(G) is nilpotent if and only if |ab|=|a||b| for any powers of γ*k -commutators a,bϵG of coprime orders (Theorem B).
Coprime commutators in finite groups
Monetta C.
2019-01-01
Abstract
Let G be a finite group and let k≥2 We prove that the coprime subgroup γ*k(G) is nilpotent if and only if |xy|=|x||y| for any γ*k -commutators x,yϵG of coprime orders (Theorem A). Moreover, we show that the coprime subgroup γ*k(G) is nilpotent if and only if |ab|=|a||b| for any powers of γ*k -commutators a,bϵG of coprime orders (Theorem B).File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
