On a maximal subgroup of the Thompson simple group

The present paper deals with a maximal subgroup of the Thompson group, namely the group $2^{1+8}_{+}{^{cdot}}A_{9}:= overline{G}.$ We compute its conjugacy classes using the coset analysis method, its inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory

Some irreducible 2-modular codes invariant under the symplectic group S6(2)

We examine all non-trivial binary codes and designs obtained from the 2-modular primitive permutation representations of degrees up to 135 of the simple projective special symplectic group S6(2). The submodule lattice of the permutation modules, together with a comprehensive description of each code including the weight enumerator, the automorphism group, and the action of S6(2) is given. By considering the structures of the stabilizers of several codewords we attempt to gain an insight into the nature of some classes of codewords in particular those of minimum weight

2-modular representations of the alternating group A_8 as binary codes

Through a modular representation theoretical approach we enumerate all non-trivial codes from the 2-modular representations of A8, using a chain of maximal submodules of a permutation module induced by the action of A8 on objects such as points, Steiner S(3,4,8) systems, duads, bisections and triads. Using the geometry of these objects we attempt to gain some insight into the nature of possible codewords, particularly those of minimum weight. Several sets of non-trivial codewords in the codes examined constitute single orbits of the automorphism groups that are stabilized by maximal subgroups. Many self-orthogonal codes invariant under A8 are obtained, and moreover, 22 optimal codes all invariant under A8 are constructed. Finally, we establish that there are no self-dual codes of lengths 28 and 56 invariant under A8 and S8 respectively, and in particular no self-dual doubly-even code of length 56

On a generalization of M-group

In this paper, we will show that if for every nonlinear complex irreducible character of a finite group G, some multiple of it is induced from an irreducible character of some proper subgroup of G, then G is solvable. This is a generalization of Taketa's Theorem on the solvability of M-group.Comment: 17 pages, to appear in J. Algebr

Fischer-Clifford matrices of the generalized symmetric group - (A computational approach)

Let Zm be the cyclic group of order m and N be the direct product of ncopies of Zm. Let Sn be the symmetric group of degree n. The wreath product ofZm with Sn is a split extension of N by Sn, called the generalized symmetric group,here denoted by B(m; n). In his Ph.D. thesis Almestady presented a combinatorialmethod for constructing the Fischer-Clifford matrices of B(m; n). However as afew examples for small values of m and n show, the manual calculation of thesematrices presents formidable problems and hence a computerized approach to thiscombinatorial method is necessary. In a previous paper the current authors havegiven a computer programme that computes matrices which are row equivalent to theFischer-Clifford matrices of B(2; n). Here that programme is generalized to B(m; n),where m is any positive integer. It is anticipated that with some improvements, anumber of the programmes given here can be incorporated into GAP. Indeed withfurther development work these programmes should lead to an alternative methodfor computing the character table of B(m; n) in GAP.Mathematics Subject Classication (2010): 20C15, 20C30, 20C40, 05E15, 05E18, 20E22.Key words: Generalized symmetric group, m-compositions of n, Fischer-Clifford matrices,m-set of partition [λ]

PERMUTATION ACTIONS OF THE SYMMETRIC GROUP Sn ON THE GROUPS Zn AND Z nm

To view the abstract for this article click on the link below

A note on the affine subgroup of the symplectic 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 $Sp_6(2)$