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Abelian subgroups of p-groups.

, 1968
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Pure subgroups of non-abelian groups

Publicationes Mathematicae Debrecen, 2022
A footnote to this paper explains that it was written in 1961 and is now published to complete the record of the mathematical work of the late A. Kertész. Let n be a cardinal number. A subgroup G of a group H is called n-pure if every system of equations in the elements of G and a set of variables X with \(| X|
Kertész, A., Kovács, L. G., Neumann, B. H.   +2 more
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Coverings of Groups by Abelian Subgroups

Canadian Journal of Mathematics, 1978
Paul Erdôs has suggested an investigation of infinite groups from the point of view of the partition relations of set theory. In particular, he suggested that given a group G, one considers the graph T with vertex set G whose edges are the pairs ﹛g, h﹜ which do not commute.
Faber, V., Laver, R., McKenzie, R.
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ABELIAN SUBGROUPS OF GALOIS GROUPS

Mathematics of the USSR-Izvestiya, 1992
See the review in Zbl 0736.12004.
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Commutator Invariant Subgroups of Abelian Groups

Siberian Mathematical Journal, 2010
The commutator \([\varphi,\psi]\) of two elements of a ring is the element \(\varphi\psi-\psi\varphi\). A subgroup \(H\) of an Abelian group \(A\) is commutator invariant if \([\varphi,\psi]H\subseteq H\) for all commutators in the endomorphism ring of \(A\).
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Subgroups of Bounded Abelian Groups

1984
Valuated groups are a topic of central interest in Abelian group theory. On one hand, they provide a viewpoint for classical Abelian theory problems, and on the other hand are of interest in their own right. In this latter regard, there has been some progress in getting structure theorems for certain valuated groups.
Roger Hunter, Fred Richman, Elbert Walker   +2 more
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SYMMETRIC GROUPS AS PRODUCTS OF ABELIAN SUBGROUPS

Bulletin of the London Mathematical Society, 2002
Summary: A proof is given that the full symmetric group over any infinite set is the product of finitely many Abelian subgroups. In fact, 289 subgroups suffice. Sharp bounds are also obtained on the minimal number \(k\), such that the finite symmetric group \(S_n\) is the product of \(k\) Abelian subgroups.
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Intersection of Abelian subgroups in finite groups

Mathematical Notes, 1994
Let \(G\) be a finite group with subgroups \(A\) and \(B\). The author of the paper under review calls minimal elements (with respect to inclusion) of the set \(\{A^g\cap B\mid g\in G\}\) minimal \((A, B)\)-intersections. Generalizing results of \textit{T. J. Laffey} [Proc. Edinb. Math. Soc., II. Ser. 20 (1976), 229-232 (1977; Zbl 0363.20021)], \textit{
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Honest subgroups of abelian groups

Rendiconti del Circolo Matematico di Palermo, 1963
Abian, A., Rinehart, D.
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Subgroups of Abelian Polish Groups

2006
2. Notation In what follows, G is an uncountable abelian Polish group and d(·, ·) a compatible, complete, two sided-invariant metric. We write the group operations on G with reference to it being abelian – thus + is the group operation and n · g stands for g + g + · · · (n times) · · ·+ g. 0 is the group identity in G. We will find it convenient to use
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