in this paper we give some general results on the non-splitextension group $overline{g}_{n} = 2^{2n}{^{cdot}}sp(2n,2), ngeq2.$ we then focus on the group $overline{g}_{4} =2^{8}{^{cdot}}sp(8,2).$ we construct $overline{g}_{4}$ as apermutation group acting on 512 points. the conjugacy classes aredetermined using the coset analysis technique. then we determine theinertia factor groups and fischer...

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

The ordinary character table and the (cha.ta.) of rational representations (ra.repr.) for projective special linear groups                   (2,41)  (2,43) find in this work to cyclic partition each group

we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.

This paper shows how to use Computational Algebra techniques, namely the decomposition of rational functions in one variable, to explore a certain set of modular functions, called replicable functions, that arise in Monstrous Moonshine. This is an active topic in Mathematics that links the Monster group and complex analysis due to a surprising relation between the character table of the Monster...

In this paper we give some general results on the non-splitextension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq2.$ We then focus on the group $overline{G}_{4} =2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as apermutation group acting on 512 points. The conjugacy classes aredetermined using the coset analysis technique. Then we determine theinertia factor groups and Fischer...

0.1. Let G be a connected reductive algebraic group defined over a finite field Fq and let G(Fq) be the finite group of all Fq-rational points of G. We would like to present here a strategy for computing the character table of G(Fq) , under the assumption that p, the characteristic of Fq , is sufficiently large. We can assume that G has a simply connected derived group. Indeed, in the general c...

We construct a pair of non-commutative rank 8 association schemes from 3 non-symmetric scheme. For the pair, two have same character table but different Frobenius-Schur indicators. This situation is similar to dihedral group and quaternion order 8. also determine structures adjacency algebras them over rational number field.