SMALL DERIVED QUOTIENTS IN FINITE p-GROUPS
نویسنده
چکیده
More than 70 years ago, P. Hall showed that if G is a finite p -group such that a term G(d+1) of the derived series is non-trivial, then the order of the quotient G(d)/G(d+1) is at least p2 +1 . Recently Mann proved that, in a finite p -group, Hall’s lower bound can be taken for at most two distinct d . For odd p , we prove a sharp version of this result and characterise the groups with two small derived quotients. Dedicated to the memory of my dear friend and mentor, Edit Szabó.
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