2 votes 2 votes If the order of a group is $36$ then which of the following is a possible order of an element of a group. $5$ $7$ $6$ $10$ Set Theory & Algebra goclasses2024-dm-3-weekly-quiz goclasses set-theory&algebra group-theory 1-mark + – GO Classes asked Apr 27, 2022 retagged May 4, 2023 by Lakshman Bhaiya GO Classes 303 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes Order of element of a group divides the order of the group. $36$ is divisible by only $6$ thus only option (C) is possible. GO Classes answered Apr 27, 2022 GO Classes comment Share Follow See all 2 Comments See all 2 2 Comments reply Shubhamishere commented Mar 31, 2023 reply Follow Share also, apart from 6 there can be various other subgroups of different order. i.e order 3, 4, 9, 12, 16. If I am not wrong. 0 votes 0 votes parth023 commented Jun 1, 2023 reply Follow Share according to lagrange’s theorem 16 doesn’t divide 36, so size of subgroup 16 is not possible, and similarly you can’t comment on other possible orders of subgroup, because converse of lagrange’s theorem is not always true. 0 votes 0 votes Please log in or register to add a comment.