1 votes 1 votes Find all the subgroups of a cyclic group of order 12. (A) {e},(a6),(a4),(a3),(a2),(a) (B) (a12),(a6),(a4),(a3),(a2),(a) (C) (a12),(a6),(a4),(a2),(a) (D) (a12),(a6),(a4),(a3),(a2),(a),{e} Set Theory & Algebra discrete-mathematics group-theory set-theory&algebra + – ankitgupta.1729 asked Dec 6, 2017 ankitgupta.1729 1.1k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes for all group G ....'G' and e are trivial subgroups and now by using lagrenges theorm... ORDER OF SUBGROUP MUST DIVIDE THE ORDER OF GROUP.... so correct answer will we D) as all subgoups's degree divide the MAIN GROUPS ORDER.... SHUBHAM SHASTRI answered Dec 6, 2017 selected Feb 20, 2018 by ankitgupta.1729 SHUBHAM SHASTRI comment Share Follow See 1 comment See all 1 1 comment reply Tesla! commented May 7, 2018 reply Follow Share order of a subgroup must divide the order of group but it does not necessarily mean all that divisors are a subgroup https://youtu.be/TCcSZEL_3CQ?t=2m50s 0 votes 0 votes Please log in or register to add a comment.