0 votes 0 votes Number of non-isomorphic groups of order 10 = ? Set Theory & Algebra group-theory + – Balaji Jegan asked Oct 26, 2018 Balaji Jegan 483 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply srestha commented Oct 26, 2018 reply Follow Share Ans will be 4, with lagrange theorem 0 votes 0 votes Magma commented Oct 26, 2018 reply Follow Share srestha mam how ... How langrage theorem applied here ?? 0 votes 0 votes srestha commented Oct 26, 2018 reply Follow Share Every group of prime order has no proper ans nontrivial subgroup. So, here order 1,3,5 forms proper trivial subgroup and also nonisomorphic Now, order 10 also trivial subgroup. So, total 4 subgroup, which are trivial too So, 4 groups 1 votes 1 votes Shamim Ahmed commented Dec 6, 2018 reply Follow Share I think answer should be 1. The number of Abelian groups of order P^k (P is prime) is the number of partitions of k. When we prime factorize 10 = 2^1 * 5^1. Now we find partitions of the powers which are 1 and 1. We multiply them 1*1=1 Correct me if i am wrong. i referred to this question:- https://gateoverflow.in/1219/gate2007-21 0 votes 0 votes Please log in or register to add a comment.