Some results on the main supergraph of finite groups

Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that G ≅ PSL(2, p) or PGL(2, p) if and only if S(G) ≅ S(PSL(2, p)) or S( PGL(2, p)), respectively. Also, we...

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Опубліковано в: :	Algebra and Discrete Mathematics
Дата:	2020
Автори:	Asboei, A.K., Salehi, S.S.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут прикладної математики і механіки НАН України 2020
Онлайн доступ:	https://nasplib.isofts.kiev.ua/handle/123456789/188561
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Some results on the main supergraph of finite groups / A.K. Asboei, S.S. Salehi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 172–178. — Бібліогр.: 17 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	nasplib_isofts_kiev_ua-123456789-188561
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spelling	Asboei, A.K. Salehi, S.S. 2023-03-06T14:22:13Z 2023-03-06T14:22:13Z 2020 Some results on the main supergraph of finite groups / A.K. Asboei, S.S. Salehi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 172–178. — Бібліогр.: 17 назв. — англ. 1726-3255 DOI:10.12958/adm584 2010 MSC: 20D08; 05C25. https://nasplib.isofts.kiev.ua/handle/123456789/188561 Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) \| o(y) or o(y) \| o(x). In this paper, we will show that G ≅ PSL(2, p) or PGL(2, p) if and only if S(G) ≅ S(PSL(2, p)) or S( PGL(2, p)), respectively. Also, we will show that if M is a sporadic simple group, then G ≅ M if only if S(G) ≅ S(M). The authors would like to thank the referee for his/her careful reading and useful suggestions which led us to improve the paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Some results on the main supergraph of finite groups Article published earlier
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	Some results on the main supergraph of finite groups
spellingShingle	Some results on the main supergraph of finite groups Asboei, A.K. Salehi, S.S.
title_short	Some results on the main supergraph of finite groups
title_full	Some results on the main supergraph of finite groups
title_fullStr	Some results on the main supergraph of finite groups
title_full_unstemmed	Some results on the main supergraph of finite groups
title_sort	some results on the main supergraph of finite groups
author	Asboei, A.K. Salehi, S.S.
author_facet	Asboei, A.K. Salehi, S.S.
publishDate	2020
language	English
container_title	Algebra and Discrete Mathematics
publisher	Інститут прикладної математики і механіки НАН України
format	Article
description	Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) \| o(y) or o(y) \| o(x). In this paper, we will show that G ≅ PSL(2, p) or PGL(2, p) if and only if S(G) ≅ S(PSL(2, p)) or S( PGL(2, p)), respectively. Also, we will show that if M is a sporadic simple group, then G ≅ M if only if S(G) ≅ S(M).
issn	1726-3255
url	https://nasplib.isofts.kiev.ua/handle/123456789/188561
citation_txt	Some results on the main supergraph of finite groups / A.K. Asboei, S.S. Salehi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 172–178. — Бібліогр.: 17 назв. — англ.
work_keys_str_mv	AT asboeiak someresultsonthemainsupergraphoffinitegroups AT salehiss someresultsonthemainsupergraphoffinitegroups
first_indexed	2025-12-07T16:08:35Z
last_indexed	2025-12-07T16:08:35Z
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Some results on the main supergraph of finite groups

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