On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$
A group is said to be periodic, if any of its elements is of finite order. A Shunkov group is a group in which any pair of conjugate elements generates Finite subgroup with preservation of this property when passing to factor groups by finite Subgroups. The group $ G $ is saturated with groups from...
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Irkutsk State University
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doaj-3cb8f6e43bb044adaadaffaeee03a5bf2020-11-24T23:16:16ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика" 1997-76702541-87852017-06-0120196108https://doi.org/10.26516/1997-7670.2017.20.96On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$A. ShlepkinA group is said to be periodic, if any of its elements is of finite order. A Shunkov group is a group in which any pair of conjugate elements generates Finite subgroup with preservation of this property when passing to factor groups by finite Subgroups. The group $ G $ is saturated with groups from the set of groups $ X $ if any A finite subgroup $ K $ of $ G $ is contained in the subgroup of $ G $, Isomorphic to some group in $ X $. The paper establishes the structure of periodic groups And Shunkov groups saturated by the set of groups $\mathfrak {M} $ consisting of one finite simple non-Abelian group $ A_5 $ and dihedral groups with Sylow 2-subgroup of order 2. It is proved that A periodic group saturated with groups from $\mathfrak {M}, $ is either isomorphic to a prime Group $ A_5 $, or is isomorphic to a locally dihedral group with Sylow 2 subgroup of order 2. Also, the existence of the periodic part of the Shunkov group saturated with groups from the set $ \mathfrak {M} $ is proved, and the structure of this periodic part is established.http://isu.ru/journal/downloadArticle?article=_5da18f698508480abbd6e571cb3e7063&lang=rusPeriodic groupsgroups saturated with the set of groupsShunkov group |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
A. Shlepkin |
spellingShingle |
A. Shlepkin On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$ Известия Иркутского государственного университета: Серия "Математика" Periodic groups groups saturated with the set of groups Shunkov group |
author_facet |
A. Shlepkin |
author_sort |
A. Shlepkin |
title |
On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$ |
title_short |
On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$ |
title_full |
On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$ |
title_fullStr |
On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$ |
title_full_unstemmed |
On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and $A_5$ |
title_sort |
on periodic groups and shunkov groups that are saturated by dihedral groups and $a_5$ |
publisher |
Irkutsk State University |
series |
Известия Иркутского государственного университета: Серия "Математика" |
issn |
1997-7670 2541-8785 |
publishDate |
2017-06-01 |
description |
A group is said to be periodic, if any of its elements is of finite order.
A Shunkov group is a group in which any pair of conjugate elements generates
Finite subgroup with preservation of this property when passing to factor groups by finite
Subgroups. The group $ G $ is saturated with groups from the set of groups $ X $ if any
A finite subgroup $ K $ of $ G $ is contained in the subgroup of $ G $,
Isomorphic to some group in $ X $. The paper establishes the structure of periodic groups
And Shunkov groups saturated by the set of groups $\mathfrak {M} $ consisting of one finite simple non-Abelian group $ A_5 $ and dihedral groups with Sylow 2-subgroup of order 2.
It is proved that
A periodic group saturated with groups from $\mathfrak {M}, $ is either isomorphic to a prime
Group $ A_5 $, or is isomorphic to a locally dihedral group with Sylow 2 subgroup of order 2.
Also, the existence of the periodic part of the Shunkov group saturated with groups from the set $ \mathfrak {M} $ is proved, and the structure of this periodic part is established. |
topic |
Periodic groups groups saturated with the set of groups Shunkov group |
url |
http://isu.ru/journal/downloadArticle?article=_5da18f698508480abbd6e571cb3e7063&lang=rus |
work_keys_str_mv |
AT ashlepkin onperiodicgroupsandshunkovgroupsthataresaturatedbydihedralgroupsanda5 |
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