Title: | On the lattice of the σ-permutable subgroups of a finite group |
Authors: | Skiba, A.N. Скиба, А.Н. |
Issue Date: | 2017 |
Citation: | Skiba, A.N. On the lattice of the σ-permutable subgroups of a finite group / A.N. Skiba // arXiv.org.math.GR. - 2017. - arXiv:1703.01773v2. - P. [1-13]. |
Abstract: | Let σ = {σi|i ∈ I} be some partition of the set of all primes P, G a finite group and σ(G) = {σi|σi ∩ π(G) 6= ∅}. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member 6= 1 of H is a Hall σi-subgroup of G for some σi ∈ σ and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ(G). A subgroup A of G is said to be σ-permutable in G if G possesses a complete Hall σ-set and A permutes with each Hall σi-subgroup H of G, that is, AH = HA for all i ∈ I. We characterize finite groups with distributive lattice of the σ-permutable subgroups. |
URI: | http://elib.gsu.by/jspui/handle/123456789/17297 |
Appears in Collections: | Статьи |
Files in This Item:
File | Description | Size | Format | |
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Skiba_On_the_lattice.pdf | 168.26 kB | Adobe PDF | View/Open |
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