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Some characterizations for some sporadic simple groups
Wir identifizieren Co1, M(24)' und die Monstergruppe anhand ihrer 3-lokalen Information. Sei G eine endliche Gruppe und H1 und H2 zwei Untergruppen von G, so dass H1 der Normalisator eines 3-zentralen Elements von G ist und H2 der Normalisator einer maximal elementar abelschen 3-Gruppe in G ist. In dieser Dissertation beweisen wir, dass falls H1 die Form 31+12.2Suz : 2, H2 die Form 38 : Ω8- (3) und H1∩H2 die Form 38.36.2U4(3) : 2 hat, dann ist G isomorph zur Monstergruppe. Falls H1 die Form 31+10.U5(2) : 2, H2 die Form 37Ω7(3) und H1 ∩ H2 die Form 37.35.U4(2) : 2 hat, dann ist G ≅ M(24)'. Falls H1 die Form 31+4.Sp4(3) : 2, H2 die Form 36 : 2M12 und H1 ∩ H2 die Form 36.32.(GL2(3) × 2) hat, dann ist G ≅ Co1. Also identifizieren wir die Gruppe M(24)' mit der Struktur des Normalisators eines 3-zentralen Elements. ; We identify Co1, M(24)' and the Monster group from their 3-local information. Let G be a finite group and H1 and H2 be two subgroups of G such that H1 is the normalizer of a 3-central element in G and H2 is the normalizer of a maximal elementary abelian 3-group in G. In this thesis we show that if H1 has shape 31+12:2Suz : 2, H2 has shape 38 : Ω8- (3) and H1∩H2 has shape 38:36:2U4(3) : 2, then G is isomorphic to the Monster group. If H1 has shape 31+10:U5(2) : 2, H2 has shape 37Ω7(3) and H1 ∩ H2 has shape 37:35:U4(2) : 2, then G ≅ M(24)'. If H1 has shape 31+4:Sp4(3) : 2, H2 has shape 36 : 2M12 and H1 ∩ H2 has shape 36:32:(GL2(3) × 2), then G ≅ Co1. Also we identify the group M(24)' by the structure of the normalizer of a 3-central element. ; von Mohammad Reza Salarian
Some characterizations for some sporadic simple groups
Wir identifizieren Co1, M(24)' und die Monstergruppe anhand ihrer 3-lokalen Information. Sei G eine endliche Gruppe und H1 und H2 zwei Untergruppen von G, so dass H1 der Normalisator eines 3-zentralen Elements von G ist und H2 der Normalisator einer maximal elementar abelschen 3-Gruppe in G ist. In dieser Dissertation beweisen wir, dass falls H1 die Form 31+12.2Suz : 2, H2 die Form 38 : Ω8- (3) und H1∩H2 die Form 38.36.2U4(3) : 2 hat, dann ist G isomorph zur Monstergruppe. Falls H1 die Form 31+10.U5(2) : 2, H2 die Form 37Ω7(3) und H1 ∩ H2 die Form 37.35.U4(2) : 2 hat, dann ist G ≅ M(24)'. Falls H1 die Form 31+4.Sp4(3) : 2, H2 die Form 36 : 2M12 und H1 ∩ H2 die Form 36.32.(GL2(3) × 2) hat, dann ist G ≅ Co1. Also identifizieren wir die Gruppe M(24)' mit der Struktur des Normalisators eines 3-zentralen Elements. ; We identify Co1, M(24)' and the Monster group from their 3-local information. Let G be a finite group and H1 and H2 be two subgroups of G such that H1 is the normalizer of a 3-central element in G and H2 is the normalizer of a maximal elementary abelian 3-group in G. In this thesis we show that if H1 has shape 31+12:2Suz : 2, H2 has shape 38 : Ω8- (3) and H1∩H2 has shape 38:36:2U4(3) : 2, then G is isomorphic to the Monster group. If H1 has shape 31+10:U5(2) : 2, H2 has shape 37Ω7(3) and H1 ∩ H2 has shape 37:35:U4(2) : 2, then G ≅ M(24)'. If H1 has shape 31+4:Sp4(3) : 2, H2 has shape 36 : 2M12 and H1 ∩ H2 has shape 36:32:(GL2(3) × 2), then G ≅ Co1. Also we identify the group M(24)' by the structure of the normalizer of a 3-central element. ; von Mohammad Reza Salarian
Some characterizations for some sporadic simple groups
Salarian, Mohammad Reza (author)
2008-01-01
Theses
Electronic Resource
English
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