论文标题
Schur倍增器，Bogomolov乘数和在等异形的变体下的发电机数量最少的不变性
Invariance of Schur multiplier, Bogomolov multiplier and the minimal number of generators under a variant of isoclinism
论文作者
论文摘要
我们介绍了$ Q $ -Bogomolov乘数作为Bogomolov乘数的概括，我们证明它在$ q $ isoclinism下是不变的。我们证明，$ q $ -schur乘数在$ q $ - 外部等线性下是不变的，并且很容易结果，我们证明，在外部等速线上，Schur乘数是不变的。我们还证明，如果$ g $，$ h $是$ p $ groups和$ g/z^{\ wedge}（g）\ cong h/z^{\ wedge}（h）$，则是$ g $和$ h $的最小生成器的基数。此外，我们证明了一些关于$ q $ - nonabelian张量的群组的结构性结果。
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.
