Characterizations of finite groups by sets of orders of their elements

Mazurov, V. D.

doi:10.1007/bf02671951

Cited by 110 publications

(30 citation statements)

References 5 publications

Supporting

Mentioning

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Order By: Relevance

“…Lemma 8 [23]. Let G be a finite group, N a normal subgroup of G, and G/N a Frobenius group with Frobenius kernel F and cyclic complement C. If (|F |, |N |) = 1 and F is not contained in NC G (N )/N then p|C| ∈ ω(G) for some prime divisor p of |N |.…”

Section: Preliminary Resultsmentioning

confidence: 98%

Recognition by Spectrum of Some Linear Groups over the Binary Field

Lucido

Moghaddamfar

2006

Sib Math J

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Section: Preliminary Resultsmentioning

confidence: 98%

Recognition by Spectrum of Some Linear Groups over the Binary Field

Lucido

Moghaddamfar

2006

Sib Math J

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“…Lemma 2.8 [19,Lemma 1]. Let N be a normal subgroup of G. Assume that G/N is a Frobenius group with a Frobenius kernel F and a cyclic Frobenius complement C. If |N |, |F | = 1, and F is not contained in…”

Section: Preliminary Resultsmentioning

confidence: 98%

Quasirecognition by prime graph of the simple group 2 F 4(q)

2009

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As the main result, we show that if G is a nite group such that Γ(G) = Γ 2 F4(q) , where q = 2 2m+1 for some m 1, then G has a unique nonabelian composition factor isomorphic to 2 F4(q). We also show that if G is a nite group satisfying |G| = 2 F4(q) and Γ(G) = Γ 2 F4(q) , then G ∼ = 2 F4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2 F4(q).

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“…The following result, which belongs to Mazurov [5,Lemma 1], is often used for solving the problem of recognition of finite groups by spectrum or prime graph.…”

Section: Proposition 12 Suppose That G Is a Finite Quasi-simple Gromentioning

confidence: 99%