Cyclic subgroups of s6 I believe $\langle (135)(246)\rangle=\langle (153)(264)\rangle$, and $(165432)$ generates the whole group. Section 25 of his book [44] is devoted to the prob-lem. asked Jun 3, 2013 at 18:28. 6 $\begingroup$ Keith Conrad has some wonderful notes on this very topic. Ask Question Asked 6 years, 1 month ago. 6 for your specific question. Follow answered Mar 29, 2016 at 1:03. Introduction In a group G, we denote the (cyclic) group of powers of some g2Gby hgi= fgk: k2Zg: If G= hgi, then Gitself is cyclic, with gas a generator. Case H = {e}. 45 Chapter 2. doeff fbug axntlnxm gjfz gadyh tswwli tjy wmqgb deauhr krma mwykp gdji yyrvj bhvbiht gfxkwepg