Symmetric and Permutation Generating sets of S28k+r and A28+r of degree 28k+r using PSL 2,27

Abstract

In this paper, we aimed to use PSL(2,27) to generate the symmetric group S_{28k+r} and the alternating group A_{28k+r} of degree 28k+r5555. We have given symmetric and permutational generating sets of S_{28k+r} and A_{28k+r} 6, using the projective linear group $PSL(2,27)$ and an element of order $2k+r in A_{28k+r} for all integers $k\ge1$7. We also have shown that S_{28k+r} and A_{28k+r} can be symmetrically generated using some symmetric generating sets