Antonio Tortora

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 totally inert simple groups

A subgroup H of a group G is inert if |H: H ∩ Hg| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.

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.

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 Properties of Bell Groups

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

Primitivity of PRESENT and other lightweight ciphers

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