Some Inequalities for Nilpotent Multipliers of Powerful $p$-Groups

Details Some Inequalities for Nilpotent Multipliers of Powerful $p$-Groups Some Inequalities for Nilpotent Multipliers of Powerful $p$-Groups

2010-12-15

arxiv.org/abs/1012.3243v1

Bulletin of the Iranian Mathematical Society, Vol. 33 No. 2 (2007), pp 61-71

Mathematics

Group Theory

14 pages

Scientific paper

In this paper we present some inequalities for the order, the exponent, and the number of generators of the c-nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups of class at most $c \geq 1$) of a powerful p-group. Our results extend some of Lubotzky and Mann$^{,}$s (Journal of Algebra, 105 (1987), 484-505.) to nilpotent multipliers. Also, we give some explicit examples showing the tightness of our results and improvement some of the previous inequalities.

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