Strongly imbedded infinitely isolated subgroup of a periodic group

1983 ◽  
Vol 22 (2) ◽  
pp. 88-95 ◽  
Author(s):  
A. N. Izmailov
Keyword(s):  
Periodic Group ◽  
Isolated Subgroup

scholarly journals On p-Separability of Subgroups of Free Metabelian Groups

2006 ◽  
Vol 13 (02) ◽  
pp. 289-294 ◽  
Author(s):  
Valerij G. Bardakov
Keyword(s):  
Prime Number ◽  
Cyclic Group ◽  
Nilpotent Groups ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Isolated Subgroup

We prove that every free metabelian non-cyclic group has a finitely generated isolated subgroup which is not separable in the class of nilpotent groups. As a corollary, we prove that for every prime number p, an arbitrary free metabelian non-cyclic group has a finitely generated p′-isolated subgroup which is not p-separable.

On the Residual Finiteness of Polygonal Products of Nilpotent Groups

1992 ◽  
Vol 35 (3) ◽  
pp. 390-399 ◽  
Author(s):  
Goansu Kim ◽  
C. Y. Tang
Keyword(s):  
Nilpotent Groups ◽  
Vertex Group ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Residually Finite ◽  
Cyclic Subgroups ◽  
Isolated Subgroup ◽  
Torsion Free

AbstractIn general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.

scholarly journals On the Fundamental Physical Constants: II. Field Coupling Geometry

2017 ◽  
Vol 9 (5) ◽  
pp. 62
Author(s):  
Ogaba Philip Obande
Keyword(s):  
Internal Structure ◽  
Periodic Group ◽  
Fundamental Constant ◽  
Physical Property ◽  
Fundamental Physical Constants ◽  
Physical Constants ◽  
Field Coupling ◽  
Fundamental Physical

We show that the chemical periodic group is geometric and that the fundamental constant FC is an intrinsic physical property of the atom, it is geometric, an invariant 3-D slice of spacetime that constitutes internal structure of the atom.

The Hypercentre and the n-Centre of the Unit Group of an Integral Group Ring

1998 ◽  
Vol 50 (2) ◽  
pp. 401-411 ◽  
Author(s):  
Yuanlin Li
Keyword(s):  
Group Ring ◽  
Periodic Group ◽  
Unit Group ◽  
Complete Characterization ◽  
Integral Group Ring ◽  
Integral Group

AbstractIn this paper, we first show that the central height of the unit group of the integral group ring of a periodic group is at most 2. We then give a complete characterization of the n-centre of that unit group. The n-centre of the unit group is either the centre or the second centre (for n ≥ 2).

Subgroups like Wielandt's in finite soluble groups

1990 ◽  
Vol 107 (2) ◽  
pp. 239-259 ◽  
Author(s):  
R. A. Bryce
Keyword(s):  
Internal Structure ◽  
Direct Product ◽  
Periodic Group ◽  
Quaternion Group ◽  
Soluble Groups ◽  
Parent Group ◽  
Dedekind Group ◽  
Points Of View ◽  
Hamiltonian Groups

In 1935 Baer[1] introduced the concept of kern of a group as the subgroup of elements normalizing every subgroup of the group. It is of interest from three points of view: that of its structure, the nature of its embedding in the group, and the influence of its internal structure on that of the whole group. The kern is a Dedekind group because all its subgroups are normal. Its structure is therefore known exactly (Dedekind [7]): if not abelian it is a direct product of a copy of the quaternion group of order 8 and an abelian periodic group with no elements of order 4. As for the embedding of the kern, Schenkman[13] shows that it is always in the second centre of the group: see also Cooper [5], theorem 6·5·1. As an example of the influence of the structure of the kern on its parent group we cite Baer's result from [2], p. 246: among 2-groups, only Hamiltonian groups (i.e. non-abelian Dedekind groups) have nonabelian kern.

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