Maria Tota

On groups admitting a word whose values are Engel

Let m, n be positive integers, v a multilinear commutator word and w = vm. We prove that if G is a residually finite group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover, we show that if u is a non-commutator word and G is a locally graded group in which all u-values are n-Engel, then the verbal subgroup u(G) is locally nilpotent.

On locally graded groups with a word whose values are Engel

Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a locally graded group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent.

Groups with a Finite Number of Normalizer Subgroups

Abstract The groups having exactly one normalizer are well-known. They are the Dedekind groups. All finite groups having exactly two normalizers were classified by M. D. Pérez-Ramos and, in a recent paper, S. Camp-Mora generalized that result to locally finite groups. In this paper, we will characterize arbitrary groups with a finite number of normalizers and we will investigate the properties of arbitrary groups with two, three and four normalizers.

Some restrictions on normalizers or centralizers in finite p-groups

We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |NG(H):H|≤pk for every H

ON GROUPS WITH ALL SUBGROUPS SUBNORMAL OR SOLUBLE OF BOUNDED DERIVED LENGTH

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Some finiteness conditions on normalizers or centralizers in groups

G, (ii) |NG(〈g〉):〈g〉|≤pk for every 〈g〉

Locally Graded Quotients of Locally Graded Groups

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