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

In this paper, we aimed to use PSL (2,27) to generate the symmetric group S28k +r and the alternating group A28k +r . we have given symmetric and permutational generating sets of S28k +r and A28k +r of degree 28k + r using the projective linear group PSL (2,27) and an element of order 2k + r in S28k +r and A28k +r for all integers k≥1 . We also have shown that S28k +r and A28k +r can be symmetrically generated using some symmetric generating sets.