Displaying similar documents to “Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups”

On residually finite groups and their generalizations

Andrzej Strojnowski (1999)

Colloquium Mathematicae

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The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions...

On minimal non--groups

Francesco Russo, Nadir Trabelsi (2009)

Annales mathématiques Blaise Pascal

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A group G is said to be a -group, if G / C G ( x G ) is a polycyclic-by-finite group for all x ∈ G . A minimal non--group is a group which is not a -group but all of whose proper subgroups are -groups. Our main result is that a minimal non--group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

Bartholdi, Laurent, Grigorchuk, Rostislav (2002)

Serdica Mathematical Journal

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* 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....

Sylow 2-subgroups of solvable Q-groups.

Mohammad Reza Darafsheh, H. Sharifi (2007)

Extracta Mathematicae

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A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group.

Normal Subgroup of Product of Groups

Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama (2011)

Formalized Mathematics

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In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.