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- W2073630326 abstract "Abstract A group G is n-central if G n ≤ Z ( G ), that is the subgroup of G generated by n -powers of G lies in the centre of G . We investigate p k -central groups for p a prime number. For G a finite group of exponent p k , the covering group of G is p k -central. Using this we show that the exponent of the Schur multiplier of G is bounded by $p^{lceil frac{c}{p-1} rceil}$ , where c is the nilpotency class of G . Next we give an explicit bound for the order of a finite p k -central p -group of coclass r . Lastly, we establish that for G , a finite p -central p -group, and N , a proper non-maximal normal subgroup of G , the Tate cohomology H n ( G/N, Z(N) ) is non-trivial for all n . This final statement answers a question of Schmid concerning groups with non-trivial Tate cohomology." @default.
- W2073630326 created "2016-06-24" @default.
- W2073630326 creator A5040799296 @default.
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- W2073630326 date "2013-02-25" @default.
- W2073630326 modified "2023-09-25" @default.
- W2073630326 title "A NOTE ON p-CENTRAL GROUPS" @default.
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- W2073630326 doi "https://doi.org/10.1017/s0017089512000687" @default.
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