Symmetric and permutational generating sets of \(S_{20k+r}\) and \(A_{20k+r}\) using the projective linear group \(\text{PSL}(2,19)\). (English) Zbl 1222.20004
Summary: We show how to generate \(S_{20k+r}\) and \(A_{20k+r}\) using the projective linear group \(\text{PSL}(2,19)\) and an element of order \(2k+r\) in \(S_{20k+r}\) and \(A_{20k+r}\) for all positive integers \(k\geq 1\) and \(r\geq 1\). We also show how to generate \(S_{20k+r}\) and \(A_{20k+r}\) symmetrically using symmetric generating sets.
