Homology of Borel Subgroup of SL(2,\mathbb{F}_p) | Zendy

Bui Anh Tuan | Zendy; Bao Quoc Vo | Zendy

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Homology of Borel Subgroup of SL(2,\mathbb{F}_p)

Author(s) -

Bui Anh Tuan,

Bao Quoc Vo

Publication year - 2019

Publication title -

science and technology development journal

Language(s) - English

Resource type - Journals

ISSN - 1859-0128

DOI - 10.32508/stdj.v22i3.1225

Subject(s) - mathematics , homology (biology) , invariant (physics) , prime (order theory) , combinatorics , spectral sequence , order (exchange) , pure mathematics , mathematical physics , biochemistry , chemistry , cohomology , gene , finance , economics

In this paper we compute the integral homology of the Borel subgroup $B$ of the special linear group $SL(2,\mathbb{F}_p), p$ is a prime number. Arcoding to Adem \cite{AJM} these are periodic groups. In order to compute the integral homology of $B,$ we decompose it into $\ell-$ primary parts. We compute the first summand based on Invariant Theory and compute the rest summand based on Lyndon-Hochschild-Serre spectral sequence. We assume that $p$ is an odd prime and larger than $3.$

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