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Recognition of the groups L₅(4) and U₄(4) by the prime graph
Let G be a finite group. The prime graph of G is the graph Γ(G) whose set of vertices is the set Π(G) of all prime divisors of the order |G| and two different vertices p and q of which are connected by an edge if G has an element of order pq. We prove that if S is one of the simple groups L₅(4) and...
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Інститут математики НАН України
2012
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| Series: | Український математичний журнал |
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/164169 |
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irk-123456789-1641692020-02-23T18:27:38Z Recognition of the groups L₅(4) and U₄(4) by the prime graph Nosratpour, P. Darafsheh, M.R. Статті Let G be a finite group. The prime graph of G is the graph Γ(G) whose set of vertices is the set Π(G) of all prime divisors of the order |G| and two different vertices p and q of which are connected by an edge if G has an element of order pq. We prove that if S is one of the simple groups L₅(4) and U₄(4) and G is a finite group with Γ(G) = Γ(S), then G has a normal subgroup N such that Π(N) ⊆ {2, 3, 5} and G/N≅S. Нехай G — скiнченна група. Графом простих чисел групи G називають граф Γ(G), множиною вершин якого є множина Π(G) усiх простих дiльникiв порядку |G| i в якому двi рiзнi вершини p та q з’єднанi ребром, якщо G мiстить елемент порядку pq. Доведено, що, якщо S є однiєю з простих груп L₅(4) та U₄(4), а G є скiнченною групою, для якої Γ(G)=Γ(S), то G має нормальну пiдгрупу N таку, що Π(N)⊆{2,3,5} та G/N≅S. 2012 Article Recognition of the groups L₅(4) and U₄(4) by the prime graph / P. Nosratpour, M.R. Darafsheh // Український математичний журнал. — 2012. — Т. 64, № 2. — С. 210-217. — Бібліогр.: 21 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/164169 512.5 en Український математичний журнал Інститут математики НАН України |
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English |
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Статті Статті |
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Статті Статті Nosratpour, P. Darafsheh, M.R. Recognition of the groups L₅(4) and U₄(4) by the prime graph Український математичний журнал |
| description |
Let G be a finite group. The prime graph of G is the graph Γ(G) whose set of vertices is the set Π(G) of all prime divisors of the order |G| and two different vertices p and q of which are connected by an edge if G has an element of order pq. We prove that if S is one of the simple groups L₅(4) and U₄(4) and G is a finite group with Γ(G) = Γ(S), then G has a normal subgroup N such that Π(N) ⊆ {2, 3, 5} and G/N≅S. |
| format |
Article |
| author |
Nosratpour, P. Darafsheh, M.R. |
| author_facet |
Nosratpour, P. Darafsheh, M.R. |
| author_sort |
Nosratpour, P. |
| title |
Recognition of the groups L₅(4) and U₄(4) by the prime graph |
| title_short |
Recognition of the groups L₅(4) and U₄(4) by the prime graph |
| title_full |
Recognition of the groups L₅(4) and U₄(4) by the prime graph |
| title_fullStr |
Recognition of the groups L₅(4) and U₄(4) by the prime graph |
| title_full_unstemmed |
Recognition of the groups L₅(4) and U₄(4) by the prime graph |
| title_sort |
recognition of the groups l₅(4) and u₄(4) by the prime graph |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| topic_facet |
Статті |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/164169 |
| citation_txt |
Recognition of the groups L₅(4) and U₄(4) by the prime graph / P. Nosratpour, M.R. Darafsheh // Український математичний журнал. — 2012. — Т. 64, № 2. — С. 210-217. — Бібліогр.: 21 назв. — англ. |
| series |
Український математичний журнал |
| work_keys_str_mv |
AT nosratpourp recognitionofthegroupsl54andu44bytheprimegraph AT darafshehmr recognitionofthegroupsl54andu44bytheprimegraph |
| first_indexed |
2023-10-18T22:12:55Z |
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2023-10-18T22:12:55Z |
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1796154933403189248 |