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1
Content available remote

The structure of finite groups and ɵ-pairs of general subgroups

100%
Xu Y., Hou H., Zhang X.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
Using the concept of ɵ-pairs of proper subgroups of a finite group, we obtain some critical conditions of the supersolvability and nilpotency of finite groups.
2
Content available remote

Perfect codes in power graphs of finite groups

88%
Ma X., Fu R., Lu X., Guo M., Zhao Z.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1440-1449
EN
The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the group, in which two vertices are adjacent if they generate a cyclic subgroup. In this paper, we give a complete description of finite groups with enhanced power graphs admitting a perfect code. In addition, we describe all groups in the following two classes of finite groups: the class of groups with power graphs admitting a total perfect code, and the class of groups with enhanced power graphs admitting a total perfect code. Furthermore, we characterize several families of finite groups with power graphs admitting a perfect code, and several other families of finite groups with power graphs which do not admit perfect codes.
3
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On Hall subgroups of a finite group

75%
Guo W., Skiba A.
Open Mathematics
|
2013
|
tom 11
|
nr 7
1177-1187
EN
New criteria of existence and conjugacy of Hall subgroups of finite groups are given.
4
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Algorithms for permutability in finite groups

63%
Ballester-Bolinches A., Cosme-Llópez E., Esteban-Romero R.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1914-1922
EN
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.
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