On the asymptotic behaviour of the number of subgroups of finite abelian groups

Consequently, the set of SE-supplemented subgroups of a group is also wider than the set of all S-quasinormal subgroups, the set of weakly S- permutable subgroups, the set of

Ezquerro has given the following converse argu- ment (see [[5], Theorem D]): if there exists a normal solvable subgroup E of G such that G=E is supersolvable and all maximal

We get a very concrete criterion for a subgroup of W to embed in B/[P, P ] in terms of the stabilizers of the hyperplanes of W (Theorem 2); for the case of the symmetric group S n

Given a subgroup H of G , Linnell's result can be generalized as follows: the pair (G, H) splits as a nite graph of groups with nite edge groups such that each vertex group is nite

Keywords: Infinite subsets, finite depth, Engel groups, minimal condition on normal sub- groups, finite-by-nilpotent groups, finitely generated hyper-(Abelian-by-finite)

A close look at the proof of this result shows that the assumption that K is pure can be replaced by the weaker one that NcK\ An immediate consequence is the classical theorem

LEMMA 1.. ON ISOTYPE SUBGROUPS OF ABELIAN GROUPS. — If H is p^pure, then clearly the elements in H[p~\ have the desired property.. Then H is iso- type in G if and only if the

COROLLARY 11: The theory of abelian groups with four predicates denoting subgroups is undecidable.. Kozlov and Kokorin [4] showed that the theory of