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.

1. B. Baumslag and J. Wiegold, A sufficient condition for nilpotency in a finite group, preprint (2014), https://arxiv.org/abs/1411.2877v1.

2. R. Bastos and P. Shumyatsky, A sufficient condition for nilpotency of the commutator subgroup, Sib. Math. J. 57 (2016), no. 5, 762–763.

3. D. Gorenstein, Finite Groups, 2nd ed., Chelsea Publishing, New York, 1980.

4. M. Kassabov and N. Nikolov, Words with few values in finite simple groups, Q. J. Math. 64 (2013), no. 4, 1161–1166.

5. D. J. S. Robinson, A Course in the Theory of Groups, Grad. Texts in Math. 80, Springer, New York, 1993.

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