Remark on subgroup intersection graph of finite abelian groups

Let be a finite group. The subgroup intersection graph of is a graph whose vertices are non-identity elements of and two distinct vertices and are adjacent if and only if , where is the cyclic subgroup of generated by . In this paper, we show that two finite abelian groups are isomorphic if and only...

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Published inOpen mathematics (Warsaw, Poland) Vol. 18; no. 1; pp. 1025 - 1029
Main Authors Zhao, Jinxing, Deng, Guixin
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 18.09.2020
De Gruyter Poland
Subjects
05C25
Apexes
finite abelian group
Graph theory
Group theory
Intersections
isomorphic
subgroup intersection graph
Subgroups
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Summary:Let be a finite group. The subgroup intersection graph of is a graph whose vertices are non-identity elements of and two distinct vertices and are adjacent if and only if , where is the cyclic subgroup of generated by . In this paper, we show that two finite abelian groups are isomorphic if and only if their subgroup intersection graphs are isomorphic.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2020-0066