Results 191 to 200 of about 2,666 (229)

On Pure-High Subgroups of Abelian Groups

Canadian Mathematical Bulletin, 1974
Fuchs, in [3], problem 14, proposes the study of pure-high subgroups of an abelian group. In this paper we show that in abelian torsion groups, pure-high subgroups are also high. A natural problem arises, that of characterizing the pure-absolute summands.
K. Benabdallah
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p-Groups with maximal elementary abelian subgroups of rank 2 [PDF]

Journal of Algebra, 2010
Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2.
George Glauberman, Nadia Mazza
exaly   +2 more sources

Connected components of the category of elementary abelian p-subgroups [PDF]

Journal of Algebra, 2008
We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank $2$ in a finite $p$-group $G$, for an odd prime $p$. Namely, it is $p$ if $G$ has rank at least $3$ and it is $p+1$ if $G$ has rank $2$.
Nadia Mazza
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On Groups Saturated with Abelian Subgroups

International Journal of Algebra and Computation, 1998
Groups with the weak maximal condition on non-abelian subgroups are the main subject of this research. Locally finite groups with this property are abelian or Chemikov. Non-abelian groups with the weak maximal condition on non-abelian subgroups, which have an ascending series of normal subgroups with locally nilpotent or locally finite factors, are ...
Lev S. Kazarin, Leonid A. Kurdachenko, Igor Ya. Subbotin   +2 more
openaire   +2 more sources

Counting maximal abelian subgroups of p-groups

Archiv Der Mathematik, 2022
We show that the number of maximal abelian subgroups of afinite p-group is congruent to 1 modulo p. Furthermore, if p > 2, thesame can be said for the maximal elementary abelian subgroups, andmore generally, for the maximal abelian subgroups of any given
I M Isaacs, Isaacs I M
exaly   +2 more sources

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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Fully inert subgroups of free Abelian groups

Periodica Mathematica Hungarica, 2014
A subgroup H of an Abelian group G is called fully inert if (φH + H)/H is finite for every φ ∈ End(G). Fully inert subgroups of free Abelian groups are characterized.
Dikran Dikranjan, Luigi Salce, Paolo Zanardo   +2 more
exaly   +2 more sources

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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ABELIAN SUBGROUPS OF GALOIS GROUPS

Mathematics of the USSR-Izvestiya, 1992
See the review in Zbl 0736.12004.
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Abelian groups as autocommutator subgroups

Rendiconti del Circolo Matematico di Palermo (1952 -), 2014
Let \(G\) be a group and let \(\Aut(G)\) denote its automorphism group. For \(g\in G\) and \(a\in\Aut(G)\), the element \([g,a]=g^{-1}g^a\) is the autocommutator of \(g\) and \(a\). For a subset \(B\) of \(\Aut(G)\) one may then consider the subgroup \([G,B]\) of \(G\) generated by the autocommutators \([g,b]\) for \(g\in G\) and \(b\in B\).
Chaboksavar, M., Farrokhi Derakhshande Ghoochan, M., Saeedi, F.   +2 more
openaire   +2 more sources