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Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.

On locally finite groups and the centralizers of automorphisms

Pavel Shumyatsky (2001)

Bollettino dell'Unione Matematica Italiana

Sia $p$ un primo, e $A$ un gruppo abeliano elementare di ordine $p^{2}$ che agisce sul $p^{'}$ -gruppo localmente finito $G$ . Supponiamo che esista un intero positivo $m$ tale che $[C_{G} (a), \underset{m}{\underset{︸}{C_{G} (b), \dots, C_{G} (b)}}] = 1$ per ogni $a, b \in A^{♯}$ . In questo articolo si dimostra che $G$ è nilpotente, con classe di nilpotenza limitata da una funzione che dipende solo da $p$ e $m$ .

On locally finite minimal non-solvable groups

Ahmet Arıkan, Sezgin Sezer, Howard Smith (2010)

Open Mathematics

In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.

On locally graded barely transitive groups

Cansu Betin, Mahmut Kuzucuoğlu (2013)

Open Mathematics

We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.

On multipliers of Heineken-Mohamed type groups

B. Bruno, R. E. Phillips (1991)

Rendiconti del Seminario Matematico della Università di Padova

On outer automorphisms of Černikov $p$ -groups

Orazio Puglisi (1990)

Rendiconti del Seminario Matematico della Università di Padova

On $p$ -groups with generally finite element.

Popov, A.M. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

Bartholdi, Laurent, Grigorchuk, Rostislav (2002)

Serdica Mathematical Journal

* The authors thank the “Swiss National Science Foundation” for its support.We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations. The Hecke algebras...

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