Some results on the main supergraph of finite groups
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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).
2008 ◽
Vol 07
(06)
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pp. 735-748
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2019 ◽
Vol 102
(1)
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pp. 77-90
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2016 ◽
Vol 09
(03)
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pp. 1650054
2019 ◽
Vol 18
(12)
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pp. 1950230
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1969 ◽
Vol 21
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pp. 965-969
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1988 ◽
Vol 108
(1-2)
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pp. 117-132
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