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A note on some special $p$-groups. (arXiv:1807.04959v1 [math.GR])
来源于:arXiv
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^{\frac{1}{2}d(d-1)}$ for $ d\geq 3 $ and $ p\neq 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^{\frac{1}{2}d(d-1)-1}$ for $ d\geq 3 $ and $ p\neq 2. $ Additionally,
when $ G $ is of exponent $ p, $ we give the structure of $ G. $ 查看全文>>