0000000000082759
AUTHOR
V. Pérez-calabuig
On formations of finite groups with the generalized Wielandt property for residuals II
A formation [Formula: see text] of finite groups has the generalized Wielandt property for residuals, or [Formula: see text] is a GWP-formation, if the [Formula: see text]-residual of a group generated by two [Formula: see text]-subnormal subgroups is the subgroup generated by their [Formula: see text]-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.
On formations of finite groups with the generalised Wielandt property for residuals
Abstract A formation F of finite groups has the generalised Wielandt property for residuals, or F is a GWP-formation, if the F -residual of a group generated by two F -subnormal subgroups is the subgroup generated by their F -residuals. We prove that every GWP-formation is saturated. This is one of the crucial steps in the hunt for a solution of the classification problem.
Maximal subgroups and PST-groups
A subgroup H of a group G is said r 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 groups, and maxmial subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25)] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions o…
The Abelian Kernel of an Inverse Semigroup
The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.
An Elementary Proof of a Theorem of Graham on Finite Semigroups
The purpose of this note is to give a very elementary proof of a theorem of Graham that provides a structural description of finite 0-simple semigroups and its idempotent-generated subsemigroups.
On complements of 𝔉-residuals of finite groups
ABSTRACTA formation 𝔉 of finite groups has the generalized Wielandt property for residuals, or 𝔉 is a GWP-formation, if the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉-residuals. The main aim of the paper is to determine some sufficient conditions for a finite group to split over its 𝔉-residual.