Abstract
A well-known conjecture on p-groups states that every non-abelian p-group G has the property that | G | divides | Aut ( G ) | . We exhibit periodic patterns in the automorphism group orders of the 2-groups of fixed coclass and we use this to show that for every positive integer r there are at most finitely many counterexamples to the conjecture among the 2-groups of coclass r.
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