0 votes 0 votes Let G be a non-abelian group, order of G can be ? (A) 24 (B) 44 (C) 54 (D) 34 Set Theory & Algebra abelian-group + – ankitgupta.1729 asked Dec 6, 2017 ankitgupta.1729 920 views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments Red_devil commented Dec 7, 2017 reply Follow Share https://en.wikipedia.org/wiki/List_of_small_groups#List_of_small_non-abelian_groups 0 votes 0 votes s_dr_13 commented Mar 21, 2022 reply Follow Share We know that if O(G) =prime ----» G is Abelian. If we apply the contrapositive statement, we get G is non-abelian ----» O(G) is not prime Using this, we get all options can be potential answers ?? 1 votes 1 votes ankitgupta.1729 commented Mar 25, 2022 reply Follow Share yes, all the options are correct here because we can construct the non-abelian group for each of the order of the group mentioned in the options and it is $(prime)^2$ not prime. Correct statement is every group of order $p^2$ where $p$ is prime is abelian. 0 votes 0 votes Please log in or register to add a comment.