Results 151 to 160 of about 544 (187)

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
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Almost isomorphism of Abelian groups and determinability of Abelian groups by their subgroups

Journal of Mathematical Sciences, 2006
A group \(A\) is determined by its subgroups if for any group \(B\) the existence of a bijection between the subgroups of \(A\) and \(B\) with the property that image and preimage of this bijection are always isomorphic, implies that \(A\cong B\). \(A\) is called a correct Abelian group if for any group \(B\) we can conclude from \(A\cong B'\) and \(B ...
Grinshpon, S. Ya., Mordovskoi, A. K.
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Groups with small abelian subgroups

Archiv der Mathematik, 1988
If \(S\) is a subgroup of \(G\) such that \(SZ(G)/Z(G)\) is cyclic, then \(S\) is abelian. The author classifies those finite \(p\)-groups in which all subgroups are of this sort; he shows that in this case \(G/Z(G)\) is either elementary abelian or dihedral or non-abelian of order \(p^3\) and of exponent \(p\).
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Dominions in abelian subgroups of metabelian groups

Algebra and Logic, 2012
Let \(\mathcal M\) be a quasivariety of groups. If \(A\in\mathcal M\) and \(H\leq A\) then the dominion of \(H\) is \(\text{dom}_A^{\mathcal M}(H)=\{a\in A\mid\text{for all }M\in\mathcal M,\text{ for all }f,g\colon A\to M,\text{ if }f|_H=g|_H\text{ then }a^f=a^g\}\).
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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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On strongly invariant subgroups of Abelian groups

Mathematical Notes, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Honest subgroups of abelian groups

Rendiconti del Circolo Matematico di Palermo, 1963
Abian, A., Rinehart, D.
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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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