Results 201 to 210 of about 2,666 (229)

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.
openaire   +2 more sources

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 \(p\).
openaire   +2 more sources

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 \(\text{dom}_A^{\mathcal M}(H)=\{a\in A\mid\text{for all }M\in\mathcal M,\text{ for all }f,g\colon A\to M,\text{ if }f|_H=g|_H\text{ then }a^f=a^g\}\).
openaire   +2 more sources

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{
openaire   +1 more source

On strongly invariant subgroups of Abelian groups

Mathematical Notes, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

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 \(A\).
openaire   +2 more sources

Honest subgroups of abelian groups

Rendiconti del Circolo Matematico di Palermo, 1963
Abian, A., Rinehart, D.
openaire   +1 more source

SIMULTANEOUS DECOMPOSITIONS OF AN ABELIAN GROUP AND A SUBGROUP

The Quarterly Journal of Mathematics, 1985
Let B be a subgroup of the arbitrary abelian group C. A simultaneous decomposition of B and C is a pair of decompositions \(B=\oplus_{i\in I}B_ i\) and \(C=\oplus_{i\in I}C_ i\) such that \(B_ i=B\cap C_ i\) for each i. The question of simultaneous decompositions is attacked in the case that C is a (mixed) direct sum of cyclic groups and B is a pure ...
openaire   +2 more sources

ON ABELIAN GROUPS HAVING ISOMORPHIC PROPER CHARACTERISTIC SUBGROUPS

Journal of Commutative Algebra, 2023
Andrey R Chekhlov, Peter V Danchev
exaly  

On the Separability of Abelian Subgroups of the Fundamental Groups of Graphs of Groups. I

Siberian Mathematical Journal, 2023
E V Sokolov, Sokolov E V
exaly