Back to Search Start Over

Finite groups with the same power graph.

Authors :
Mirzargar, M.
Scapellato, R.
Source :
Communications in Algebra; 2022, Vol. 50 Issue 4, p1400-1406, 7p
Publication Year :
2022

Abstract

The power graph P(G) of a group G is a graph with vertex set G, where two vertices u and v are adjacent if and only if u ≠ v and u m = v or v m = u for some positive integer m. In this paper, we raise and study the following question: For which natural numbers n every two groups of order n with isomorphic power graphs are isomorphic? In particular, it is proved that all such odd number n are cube-free and also they are not multiples of 16 in general. Moreover, we show that if two finite groups have isomorphic power graphs and one of them is nilpotent, the same is true for the other one. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00927872
Volume :
50
Issue :
4
Database :
Complementary Index
Journal :
Communications in Algebra
Publication Type :
Academic Journal
Accession number :
155688964
Full Text :
https://doi.org/10.1080/00927872.2021.1981921