Subgroups Permutable with All Sylow Subgroups

Schmid, Peter

doi:10.1006/jabr.1998.7429

Cited by 163 publications

(68 citation statements)

References 7 publications

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“…In order to give an algorithm which allows us to decide whether or not a subgroup H of a group G is S-permutable in G, we use the following fact proved by Schmid [14] (see also [6, Proposition 1.2.18]).…”

Section: S-permutable Subgroupsmentioning

confidence: 99%

Algorithms for permutability in finite groups

2013

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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. MSC:20D10, 20D20, 20-04

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Section: S-permutable Subgroupsmentioning

confidence: 99%

Algorithms for permutability in finite groups

2013

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“…In a lot of applications in many areas of study in science and its wide application [1][2][3][4][5][6], manifold has its widespread application, for example, the theory of mechanics, electromagnetism, and field theory [7][8][9][10], etc. In applied science derived from these science manifold and has many applications, for example, ballistic engineering, aerospace engineering, a lot of projects related to electromagnetic radiation, water wave, electronic waves or magnetic wave and so on.…”

Section: Introductionmentioning

confidence: 99%

Some Notes on Orientation Preserving Involutions of Manifold

Zeng¹

2017

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Abstract. In many applied sciences, the theory of manifold plays an extremely important role, such as mechanics, electromagnetism, and field theory, etc. and in applied science derived from these sciences, manifold has many applications, it often acts as important research tools. In this article, we introduces the derivation process on involutions of the manifold, from these process, some skills are considered when the tool (i.e. manifold) can be applied.

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“…Recall that a subgroup H of G is said to be s-quasinormal in G [17] if H permutes with every Sylow subgroup of G. Following [17], we use Syl(G) ⊥ to denote the set of all s-quasinormal subgroups of G.…”

Section: Introductionmentioning

confidence: 99%