“School of Mathematics”
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Paper IPM / M / 11338  


Abstract:  
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 kfold ODcharacterizable if
there exist exactly k nonisomorphic finite groups having the
same order and degree
pattern as M. In particular, a 1fold ODcharacterizable group
is simply called ODcharacterizable. In this article, we
will show that the alternating groups A_{p+3} for p=23, 31, 37, 43 and 47 are ODcharacterizable. Moreover, we show that
the automorphism groups of these groups are 3fold
ODcharacterizable. It is worth mentioning that the prime graphs
associated with all these groups are connected.
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