Paper “On the intersection of certain maximal subgroups of a finite group” published in J. Group Theory

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Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt

On the intersection of certain maximal subgroups of a finite group

J. Group Theory, 17 (2014), 705–715

http://dx.doi.org/10.1515/jgt-2013-0052

Abstract:  Let $\Delta(G)$ denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which $G/\Delta(G)$ is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.

Paper “On the intersection of certain maximal subgroups of a finite group” to appear in J. Group Theory

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Adolfo Ballester-Bolinches, James C. Beidleman, Hermann Heineken, Matthew F. Ragland, Jack Schmidt

On the intersection of certain maximal subgroups of a finite group

J. Group Theory, in press

http://dx.doi.org/10.1515/jgt-2013-0052

Abstract:  Let $\Delta(G)$ denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which $G/\Delta(G)$ is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.

Paper “Prefactorized subgroups in pairwise mutually permutable products” published in Ann. Mat. Pura Appl.

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A. Ballester-Bolinches, J. C. Beidleman, H. Heineken, M. C. Pedraza-Aguilera

Prefactorized subgroups in pairwise mutually permutable subgroups

Ann. Math .Pura Appl., 192(6), 1043-1057 (2013)

http://dx.doi.org/10.1007/s10231-012-0257-y

Abstract

We continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist. A less stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.

MSC: 20D10, 20D20

Keywords: Finite group, Permutability, Factorization, Saturated formation.

Paper “Finite solvable groups in which semi-normality is a transitive relation” published in Beitr. Algebra Geom.

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A. Ballester-Bolinches, J. C. Beidleman, A. D. Feldman, H. Heineken, M. F. Ragland

Finite solvable groups in which semi-normality is a transitive relation

Beitr. Algebra Geom., 54(2), 549-558 (2013)

http://dx.doi.org/10.1016/j.jalgebra.2013.08.042

Abstract: A subgroup H of a finite group G is said to be seminormal in G if every Sylow p-subgroup of G, p a prime, with (|H|, p) = 1 normalizes H. A group G is called an SNT-group if seminormality is a transitive relation in G. Properties of solvable SNT-groups are studied. For example, subgroups of solvable SNT-groups are SNT-groups.
MSC: 20D05, 20D10, 20F16
Keywords: Finite groups, S-permutability, S-semipermutability, seminormal.