The cyclic subgroup separability of certain HNN extensions.
Wong, P.C., Wong, K.B. (2006)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Wong, P.C., Wong, K.B. (2006)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Archer, Claude, Cara, Philippe, Krempa, Jan (2005)
Beiträge zur Algebra und Geometrie
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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.
Dailu Li, Xiquan Liang, Yanhong Men (2010)
Formalized Mathematics
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This article describes the concept of the nilpotent group and some properties of the nilpotent groups.
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...
A. Ivanov (1999)
Colloquium Mathematicae
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We study infinite finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups. The results concern growth and the ascending chain condition for such groups.
Mikaelian, Vahagn H. (2004)
Beiträge zur Algebra und Geometrie
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W. Comfort, F. Trigos-Arrieta, S. Wu (1993)
Fundamenta Mathematicae
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The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can...
Gill, Nick (2007)
Beiträge zur Algebra und Geometrie
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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.
Xiquan Liang, Dailu Li (2009)
Formalized Mathematics
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This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group.