Camina, Rachel and Thillaisundaram, Anitha
(2013)
*A note on p-central groups.*
Glasgow Mathematical Journal, 55
(2).
pp. 449-456.
ISSN 0017-0895

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Item Type: | Article |
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Item Status: | Live Archive |

## Abstract

A group G is n-central if Gn â�¤ 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 pk , the covering group of G is pk -central. Using this we show that the exponent of the Schur multiplier of G is bounded by pâ��c/p-1â��, where c is the nilpotency class of G. Next we give an explicit bound for the order of a finite pk -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 Hn (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. Copyright Â© Glasgow Mathematical Journal Trust 2013.

Keywords: | Groups |
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Subjects: | G Mathematical and Computer Sciences > G100 Mathematics |

Divisions: | College of Science > School of Mathematics and Physics |

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ID Code: | 25190 |

Deposited On: | 08 Jan 2017 15:27 |

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