1 votes 1 votes How many different non-isomorphic Abelian groups of order 16 are there? Set Theory & Algebra group-theory + – Mk Utkarsh asked Sep 22, 2018 Mk Utkarsh 1.1k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Bhagyashree Mukherje commented Sep 22, 2018 reply Follow Share Is it 5? 0 votes 0 votes Mk Utkarsh commented Sep 22, 2018 reply Follow Share yes also please explain difference between isomorphic and non-isomorphic abelian groups 0 votes 0 votes Bhagyashree Mukherje commented Sep 22, 2018 reply Follow Share I have encountered one such problem in this link https://gateoverflow.in/1219/gate2007-21 There is a video attached in the comments about the isomorphism part but I am unable to understand it clearly 0 votes 0 votes srestha commented Aug 3, 2019 reply Follow Share @Bhagyashree Mukherje @Mk Utkarsh 1)If we want non-isomorphic and non-abelian group, then what will be ans?? 2) If we want isomorphic group of order 16, then what will be ans?? 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes The number of Abelian groups of order P^k (P is prime) is the number of partitions of k. Prime factorization of 16 = 2^4 The partitions of power i.e.., 4 = {1+1+1+1},{2+1+1},{2+2},{3+1},{4} So total partitions =5 Answer =5 Shamim Ahmed answered Dec 6, 2018 Shamim Ahmed comment Share Follow See all 0 reply Please log in or register to add a comment.