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Paper   IPM / M / 11339
School of Mathematics
  Title:   Simple groups which are 2-fold OD-characterizable
  Author(s):  A. R. Moghaddamfar (Joint with M. Akbari)
  Status:   Published
  Journal: Bull. Malaysian Math. Soc.
  Vol.:  35
  Year:  2012
  Pages:   65-77
  Supported by:  IPM
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 ODcharacterizable if hOD(G) = k. As the main results of this paper, we prove that each of the following pairs {Gl, G2} of groups:
{Bn(q),Cn(q)}, n=2m ≥ 2, |π( qn+1

q is odd prime power;
{Bp(3),Cp(3)}, |π( 3p−1

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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