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Paper
IPM / M / 11339 |
School of Mathematics
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Title: |
Simple groups which are 2-fold OD-characterizable
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Author(s): |
A. R. Moghaddamfar (Joint with M. Akbari)
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Status: |
Published
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Journal: |
Bull. Malaysian Math. Soc.
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Vol.: |
35
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Year: |
2012
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Pages: |
65-77
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Supported by: |
IPM
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Abstract: |
Let G be a finite group and D(G) be the degree pattern of G. Denote by hOD(G) the number of isomorphism classes of finite groups H satisfying (|H|,D(H))=(|G|,D(G)). A finite group G is called k-fold OD−characterizable if hOD(G) = k. As the main results of this paper, we prove that each of the following pairs {Gl, G2} of groups:
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{Bn(q),Cn(q)}, n=2m ≥ 2, |π( |
qn+1
2
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|=1 |
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q is odd prime power;
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{Bp(3),Cp(3)}, |π( |
3p−1
2
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|=1 |
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p is an odd prime,
satisfies hOD(Gi), i = 1,2. We also prove that, if (1)n = 2 and q is any prime power such
that
|π([(q2+1)/(2,q−1)])|=1 or (2)n = 2m ≥ 2 and q is a power of 2 such that
|π(qn+1)|=1, then
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