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Paper   IPM / M / 11338
School of Mathematics
  Title:   Recognizing alternating groups Ap+3 for certain primes p by their orders and degree patterns
  Author(s):  A. R. . Moghaddamfar (Joint with A. A. Hoseini)
  Status:   Published
  Journal: FMC
  Vol.:  5
  Year:  2010
  Pages:   451-553
  Supported by:  IPM
The degree pattern of a finite group M has been introduced by A. R. Moghaddamfar et al. [Algebra Colloquium, 2005, 12(3): 431?442]. A group M is called k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups having the same order and degree pattern as M. In particular, a 1-fold OD-characterizable group is simply called OD-characterizable. In this article, we will show that the alternating groups Ap+3 for p=23, 31, 37, 43 and 47 are OD-characterizable. Moreover, we show that the automorphism groups of these groups are 3-fold OD-characterizable. It is worth mentioning that the prime graphs associated with all these groups are connected.

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