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October 13, 2025Open Access

Some remarks on K₂ of finite group rings and related algebras

Key Points

The study finds explicit isomorphism formulas for K2-groups of finite abelian p-groups and cyclic p-groups.
Results demonstrate significant connections between the K2-groups and cyclic homology groups within specified structures.
Analysis includes cases where G is specifically a cyclic p-group and a finite abelian p-group, providing detailed insights.
The implications of this work may enhance understanding of algebraic structures and their homological properties.

Abstract

In this paper, a study is conducted on K₂ of the group rings with coefficient in Z/pˢZ, where the group is a finite abelian p-group G. The inverse limit of this K₂-group is also considered. Furthermore, for the first part of the study, the case where G is a cyclic p-group is addressed. Moreover, for the second part, the situation where G is a finite abelian p-group is handled. In both cases, an explicit computable isomorphism formula of the corresponding K₂-group is provided, and the results are closely related to the cyclic homology groups.

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Cite This Study

Yakun Zhang (Sun,) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d18b83 https://doi.org/https://doi.org/10.48550/arxiv.2503.00773

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