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| Paper IPM / M / 11338 |
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| Abstract: | |
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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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