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Endomorphism kernel property for finite groups

Heghine Ghumashyan, Jaroslav Guričan (2022)

Mathematica Bohemica

A group G has the endomorphism kernel property (EKP) if every congruence relation θ on G is the kernel of an endomorphism on G . In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.

Indecomposable (1,3)-groups and a matrix problem

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2013)

Czechoslovak Mathematical Journal

Almost completely decomposable groups with a critical typeset of type ( 1 , 3 ) and a p -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p k , either no indecomposables if k ≤ 2 ; only six near isomorphism types of indecomposables if k = 3 ; and indecomposables of arbitrary large rank if k ≥ 4 .

Isolated subgroups of finite abelian groups

Marius Tărnăuceanu (2022)

Czechoslovak Mathematical Journal

We say that a subgroup H is isolated in a group G if for every x ∈ G we have either x ∈ H or 〈 x 〉 ∩ H = 1 . We describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite group.

Isotype knice subgroups of global Warfield groups

Charles K. Megibben, William Ullery (2006)

Czechoslovak Mathematical Journal

If H is an isotype knice subgroup of a global Warfield group G , we introduce the notion of a k -subgroup to obtain various necessary and sufficient conditions on the quotient group G / H in order for H itself to be a global Warfield group. Our main theorem is that H is a global Warfield group if and only if G / H possesses an H ( ℵ 0 ) -family of almost strongly separable k -subgroups. By an H ( ℵ 0 ) -family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able to characterize...

Isotype subgroups of mixed groups

Charles K. Megibben, William Ullery (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of Σ -isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and p -local mixed groups. Given the history of those theories, one anticipates that definitive results are to be found only when attention is restricted to global k -groups, the prototype being global groups with decomposition bases. A large portion of this paper is...

Notes on countable extensions of  p ω + n -projectives

Peter Vassilev Danchev (2008)

Archivum Mathematicum

We prove that if G is an Abelian p -group of length not exceeding ω and H is its p ω + n -projective subgroup for n ∈ ℕ ∪ { 0 } such that G / H is countable, then G is also p ω + n -projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).

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