2022; Physical and Mathematical Sciences, 56(1 (257): 1–6
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ON SCHUR MULTIPLIERS OF SOME RELATIVELY FREE GROUPS

Grigor Gevorgyan*

Received: 2025-01-27 · Published: 2022-03-25

© 2022 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON SCHUR MULTIPLIERS OF SOME RELATIVELY FREE GROUPS
Author
Grigor Gevorgyan
Published
2022-03-25
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2022.56.1.001

Abstract

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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