A criterion for metanilpotency of a finite group-Reference-Cited by-同舟云学术

A criterion for metanilpotency of a finite group

Author:

Bastos Raimundo¹,Monetta Carmine²,Shumyatsky Pavel¹

Affiliation:

1. Departamento de Matemática , Universidade de Brasília , Brasília-DF , 70910-900 , Brazil

2. Dipartimento di Matematica , Università di Salerno , Via Giovanni Paolo II 132, 84084 Fisciano (SA) , Italy

Abstract

Abstract We prove that the kth term of the lower central series of a finite group G is nilpotent if and only if | a ⁢ b | = | a | ⁢ | b |

{|ab|=|a||b|}

for any γ k

{\gamma_{k}}

-commutators a , b ∈ G

{a,b\in G}

of coprime orders.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference6 articles.

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