On the homology of Borel subgroup of SL(2,Fp)

Tóm tắt

In the theory of algebraic groups, a Borel subgroup of an algebraic group is a maximal Zariski closed and connected solvable algebraic subgroup. In the case of the special linear group SL2 over finite fields Fp the subgroup of invertible upper triangular matrices B is a Borel subgroup. According to Adem¹ , these are periodic groups. In this paper we compute the integral homology of the Borel subgroup B of the special linear group SL(2,Fp) where p is a prime. In order to compute the integral homology of B, we decompose it into ℓ− primary parts. We compute the first summand based on Invariant Theory and compute the rest based on Lyndon-Hochschild-Serre spectral sequence. In conclusion, we found the presentation of B and its period. Furthermore, we also explicitly compute the integral homology of  B.