The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
0 votes
114 views
How many different non-isomorphic Abelian groups of order 16 are there?
in Set Theory & Algebra by Boss (34.7k points) | 114 views
0
Is it 5?
0
yes also please explain difference between isomorphic and non-isomorphic abelian groups
0

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

@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??

1 Answer

0 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

by Active (2.3k points)

Related questions

+1 vote
1 answer
1
+1 vote
1 answer
5
asked Oct 26, 2018 in Set Theory & Algebra by Balaji Jegan Active (4.8k points) | 54 views
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
49,807 questions
54,727 answers
189,302 comments
79,844 users