关于一些相对自由群的舒尔乘数

Proceedings of the YSU A: Physical and Mathematical Sciences Pub Date : 2022-03-25 DOI:10.46991/pysu:a/2022.56.1.001

Grigor Gevorgyan

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引用次数: 0

摘要

本文构造了S.I. Adian无穷基变体的自由群的中心扩展。利用这一推广证明了上述相对自由群的舒尔乘子是无限秩的自由阿贝尔群。众所周知，这些变量是由两个变量的恒等式给出的。对于固定秩$m$，这些变量的秩$m$的自由群的集合具有连续体的基数性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ON SCHUR MULTIPLIERS OF SOME RELATIVELY FREE GROUPS

In this paper central extensions of free groups of infinitely based varieties of S.I. Adian are constructed. Using this extensions we prove that the Schur multipliers of mentioned relatively free groups are free Abelian groups of infinite rank. It is well-known that these varieties are given by identities in two variables. For a fixed rank $m$, the set of free groups of rank $m$ of these varieties has the cardinality of continuum.

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Proceedings of the YSU A: Physical and Mathematical Sciences

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