A NOTE ON p-CENTRAL GROUPS
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 449-456
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A group G is n-central if Gn ≤ Z(G), that is the subgroup of G generated by n-powers of G lies in the centre of G. We investigate pk-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 $p^{\lceil \frac{c}{p-1} \rceil}$, where c is the nilpotency class of G. Next we give an explicit bound for the order of a finite 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.
CAMINA, RACHEL; THILLAISUNDARAM, ANITHA. A NOTE ON p-CENTRAL GROUPS. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 449-456. doi: 10.1017/S0017089512000687
@article{10_1017_S0017089512000687,
author = {CAMINA, RACHEL and THILLAISUNDARAM, ANITHA},
title = {A {NOTE} {ON} {p-CENTRAL} {GROUPS}},
journal = {Glasgow mathematical journal},
pages = {449--456},
year = {2013},
volume = {55},
number = {2},
doi = {10.1017/S0017089512000687},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000687/}
}
TY - JOUR AU - CAMINA, RACHEL AU - THILLAISUNDARAM, ANITHA TI - A NOTE ON p-CENTRAL GROUPS JO - Glasgow mathematical journal PY - 2013 SP - 449 EP - 456 VL - 55 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000687/ DO - 10.1017/S0017089512000687 ID - 10_1017_S0017089512000687 ER -
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