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Let $G$ be a group. If every nontrivial subgroup of $G$ has a proper supplement, then $G$ is called an $a S$ -group. We study some properties of $a S$ -groups. For instance, it is shown that a nilpotent group $G$ is an $a S$ -group if and only if $G$ is a subdirect product of cyclic groups of prime orders. We prove that if $G$ is an $a S$ -group which satisfies the descending chain condition on subgroups, then $G$ is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an $a S$ -group....

A note on supersoluble maximal subgroup and theta-pairs.

James C. Beidleman, Howard Smith (1993)

Publicacions Matemàtiques

A θ-pair for a maximal subgroup M of a group G is a pair (A, B) of subgroups such that B is a maximal G-invariant subgroup of A with B but not A contained in M. θ-pairs are considered here in some groups having supersoluble maximal subgroups.

A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups

Mario Mainardis (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$ . If $n$ is any positive integer, either odd or divisible by $4$ , then we prove that the subgroup $A^{n}$ is also quasinormal in $G$ .

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A certain property of abelian groups

A class of generalized supersoluble groups.

A conjugacy theorem for subgroups of $G L_{n}$ containing the group of diagonal matrices

A Finitely Presented Solvable Group that is not Residually Finite.

A matrix characterization of the maximal groups in $β_{X}$

A New Bound for the Genus of a Nilpotent Group

A Note on Baer Groups of Finite Rank.

A note on infinite $a S$ -groups

A note on supersoluble maximal subgroup and theta-pairs.

A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups

Abelian quasinormal subgroups of groups

Actions of groups on lattices.

Adjoint groups and the Mal'cev correspondence (a tale of four functors)

Affinities of groups

Alcuni aspetti della teoria reticolare dei gruppi infiniti

Almost finitely presented soluble groups.

Artinian and noetherian factorized groups

Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormal sind. - II

Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormal sind. - I

Automorphisms of Locally Nilpotent FC-Groups.

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