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Acta Mathematica Hungarica
Volume/Issue:
Volume 75: Issue 4
DOI:
https://doi.org/10.1023/a:1006597605945
Author:
P. Danchev
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Acta Mathematica Hungarica
Volume/Issue:
Volume 122: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-009-7178-2
Authors:
X. Guo
and
J. Wang

Abstract  

This paper gives a characterization of finite groups G in which each cyclic subgroup either is normal in G or normalizes all subgroups of G.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 131: Issue 4
DOI:
https://doi.org/10.1007/s10474-011-0073-7
Authors:
Alfred Geroldinger
,
David J. Grynkiewicz
, and
Wolfgang A. Schmid

sequences over finite abelian p -groups Rocky Mt. J. Math. 37 1541 – 1550 10.1216/rmjm/1194275933 . [10] Gao , W. , Geroldinger , A. , Schmid , W. A. 2007 Inverse zero-sum problems Acta

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 59: Issue 1
DOI:
https://doi.org/10.1007/s10998-009-9037-x
Author:
Peter Danchev

Abstract  

Let G be a p-reduced Abelian group and R a commutative unital ring of prime characteristic p such that for each natural number i the subring
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$R^{p^i }$$ \end{document}
has nilpotent elements. It is shown that if S(RG) is the normalized Sylow p-group in the group ring RG, then S(RG) is torsion-complete if and only if G is a bounded p-group. This strengthens our former results on this subject.
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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 50: Issue 2
DOI:
https://doi.org/10.1556/sscmath.50.2013.2.1239
Author:
Pál Hegedűs

In this paper we analyse the natural permutation module of an affine permutation group. For this the regular module of an elementary Abelian p-group is described in detail. We consider the inequivalent permutation modules coming from nonconjugate complements. We prove their strong structural similarity well exceeding the fact that they have equal Brauer characters.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 119: Issue 4
DOI:
https://doi.org/10.1007/s10474-007-7049-7
Authors:
M. Asaad
,
P. Csörgő
, and
M. Ramadan

Abstract  

Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω1(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω1(P) ≦ Z(P) and N G (Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 110: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-006-0004-1
Author:
Gheorghe Silberberg

Summary  

A group is called equilibratedif no subgroup Hof Gcan be written as a product of two non-normal subgroups of H. Blackburn, Deaconescu and Mann [1] investigated the finite equilibrated groups, giving a complete description of the non-soluble ones. On the other hand, they showed that the property of a finite nilpotent group of being equilibrated depends solely on the structure of its 2-generated p-subgroups. Consequently, all the finite 2-generated equilibrated p-groups were classified for any odd prime p,but the case p=2 remained unsolved. This special case will represent the subject of the present paper.

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 48: Issue 2
DOI:
https://doi.org/10.1556/sscmath.48.2011.2.1168
Authors:
Peter Danchev
and
Patrick Keef

An abelian p-group G has a nice basis if it is the ascending union of a sequence of nice subgroups, each of which is a direct sum of cyclic groups. It is shown that if G is any group, then G ⊕ D has a nice basis, where D is the divisible hull of p ω G. This leads to a consideration of the nice basis rank of G, i.e., the smallest rank of a divisible group D such that G ⊕ D has a nice basis. This concept is used to show that there exist a reduced group G and a non-reduced group H, both without a nice basis, such that G ⊕ H has a nice basis

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