If G is a finitely generated powerful pro-p group satisfying a certain law v == 1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class of G can be bounded in terms of the prime p, the number of generators of G, the law v = 1, the width of T, and the degree of the positive law. The main interest of this result is the application to verbal subgroups: if G is a p-adic analytic pro-p group in which all values of a word w satisfy positive law, and if the verbal subgroup w(G) is powerful, then w(G) is nilpotent.

Positive laws on generators in powerful pro-p groups / Acciarri, C; FERNÁNDEZ-ALCOBER G., A. - (2012), pp. 1-10. ((Intervento presentato al convegno Ischia Group Theory 2010 tenutosi a Ischia, Naples, Italy nel 14 – 17 April 2010.

Positive laws on generators in powerful pro-p groups

ACCIARRI C;
2012-01-01

Abstract

If G is a finitely generated powerful pro-p group satisfying a certain law v == 1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class of G can be bounded in terms of the prime p, the number of generators of G, the law v = 1, the width of T, and the degree of the positive law. The main interest of this result is the application to verbal subgroups: if G is a p-adic analytic pro-p group in which all values of a word w satisfy positive law, and if the verbal subgroup w(G) is powerful, then w(G) is nilpotent.
Ischia Group Theory 2010
Ischia, Naples, Italy
14 – 17 April 2010
1
10
Acciarri, C; FERNÁNDEZ-ALCOBER G., A
Positive laws on generators in powerful pro-p groups / Acciarri, C; FERNÁNDEZ-ALCOBER G., A. - (2012), pp. 1-10. ((Intervento presentato al convegno Ischia Group Theory 2010 tenutosi a Ischia, Naples, Italy nel 14 – 17 April 2010.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1255509
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