Search results for "permutable subgroup"
showing 8 items of 8 documents
Sylow permutable subnormal subgroups of finite groups
2002
[EN] An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every subnormal subgroup is permutable and Sylow permutable.
Some subgroup embeddings in finite groups: A mini review
2015
[EN] In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied. ª 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University
A note on a result of Guo and Isaacs about p-supersolubility of finite groups
2016
In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to . We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing such that , if is S-semipermutable in for all normal subgroups H of P with , then either G is p-supersoluble or else . This extends the main result of Guo and Isaacs in (Arch. Math. 105:215-222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups.
On the supersoluble hypercentre of a finite group
2016
[EN] We give some sufficient conditions for a normal p-subgroup P of a finite group G to have every G-chief factor below it cyclic. The S-permutability of some p-subgroups of O^p(G)plays an important role. Some known results can be reproved and some others appear as corollaries of our main theorems.
Algorithms for permutability in finite groups
2013
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
Z-permutable subgroups of finite groups
2016
Let Z be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called Z-permutable if H permutes with all members of Z. The main goal of this paper is to study the embedding of the Z-permutable subgroups and the influence of Z-permutability on the group structure.
On finite minimal non-nilpotent groups
2005
[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol¿fand¿s theorem on maximal Schmidt groups.
A note on finite PST-groups
2007
[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, for subgroups H and K of G with H normal in K and K normal in G, it is always the case that H is Sylow-permutable in G. In this paper, we show that finite PST-groups and finite T*-groups are one and the same. A new characterisation of soluble PST-groups is also presented.