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Subnormal, permutable, and embedded subgroups in finite groups

James Beidleman; Mathew Ragland — 2011

Open Mathematics

The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal....

Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”

James Beidleman; Mathew Ragland — 2012

Open Mathematics

The original version of the article was published in Central European Journal of Mathematics, 2011, 9(4), 915–921, DOI: 10.2478/s11533-011-0029-8. Unfortunately, the original version of this article contains a mistake: Lemma 2.1 (2) is not true. We correct Lemma 2.2 (2) and Theorem 1.1 in our paper where this lemma was used.

Pronormal and subnormal subgroups and permutability

James Beidleman; Hermann Heineken — 2003

Bollettino dell'Unione Matematica Italiana

We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow $p$ -subgroups for $p < 7$ permute with all subnormal subgroups.

On a class of finite solvable groups

James Beidleman; Hermann Heineken; Jack Schmidt — 2013

Open Mathematics

A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group...

Distributively generated near-rings with descending chain condition.

James C. Beidleman — 1966

Mathematische Zeitschrift

Formations and $π$ -closure in finite groups

James C. Beidleman — 1971

Compositio Mathematica

Closure Properties for Fitting Functors.

James C. Beidleman; Peter Hauck — 1989

Monatshefte für Mathematik

Über Fittingklassen und die Lockett-Vermutung.

James C. Beidleman; Peter Hauck — 1979

Mathematische Zeitschrift

On non-supersoluble and non-polycyclic normal subgroups

James C. Beidleman; Howard Smith — 1993

Rendiconti del Seminario Matematico della Università di Padova

Conjugate $π$ -normally embedded fitting functors

James C. Beidleman; M. Pilar Gallego — 1988

Rendiconti del Seminario Matematico della Università di Padova

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.

Maximal subgroups and PST-groups

Adolfo Ballester-Bolinches; James Beidleman; Ramón Esteban-Romero; Vicent Pérez-Calabuig — 2013

Open Mathematics

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable...