Some remarks on K₂ of finite group rings and related algebras

2025/03/02 by Zhang, Yakun
#16S34 #19C20 #19C99 #19D55 #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2503.00773

Abstract

In this paper, a study is conducted on K₂ of the group rings with coefficient in ℤ/p^sℤ, 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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• Certain Applications of the Burnside Rings and Ghost Rings in the Representation Theory of Finite Groups (II)
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