A note on some special p-groups

2018/07/13 by Johari, Farangis, Niroomand, Peyman · 1 citation
#20D15 #20E34 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1807.04959

Abstract

Recently Rai obtained an upper bound for the order of the Schur multiplier of a d-generator special p-group when its derived subgroup has the maximum value p^{(1)/(2)d(d-1)} for d≥ 3 and p≠ 2. Here we try to obtain the Schur multiplier, the exterior square and the tensor square of such p-groups. Then we specify which ones are capable. Moreover, we give an upper bound for the order of the Schur multiplier, the exterior product and the tensor square of a d-generator special p-group G when |G'|=p^{(1)/(2)d(d-1)-1} for d≥ 3 and p≠ 2. Additionally, when G is of exponent p, we give the structure of G.

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• On Projective Representations of Special p-groups

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