Schur乘子、Bogomolov乘子和最小生成元数在等倾变换下的不变性
Invariance of Schur multiplier, Bogomolov multiplier and the minimal number of generators under a variant of isoclinism
摘要：
我们引入了$q$ -Bogomolov乘子作为Bogomolov乘子的推广，并证明了它在$q$ -等倾下是不变的.证明了$q$ -Schur乘子在$q$ -外等倾下不变，并由此证明了Schur乘子在外等倾下不变.证明了若$G$，$H$是$p$ -群，且$G/Z^{\wedge}(G)\cong H/Z^{\wedge}(H)$是$p$-群，则$G$和$H$的最小生成元个数的基数相同.此外，我们还证明了群的$q$ -非交换张量平方的一些结构性结果。
英文摘要：
We introduce the $q$-Bogomolov multiplier as a generalization of the Bogomolov multiplier, and we prove that it is invariant under $q$-isoclinism. We prove that the $q$-Schur Multiplier is invariant under $q$- exterior isoclinism, and as an easy consequence we prove that the Schur multiplier is invariant under exterior isoclinism. We also prove that if $G$, $H$ are $p$-groups and $G/Z^{\wedge}(G)\cong H/Z^{\wedge}(H)$, then the cardinality of the minimal number of generators of $G$ and $H$ are the same. Moreover we prove some structural results about $q$-nonabelian tensor square of groups.
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