Open AccessHomology of Borel Subgroup of SL(2,\mathbb{F}_p)
Author(s) -
Bui Anh Tuan,
Vo Nguyen Quoc Bao
Publication year - 2019
Publication title -
khoa học công nghệ
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 $3.$