The Gateway to Computer Science Excellence
0 votes

Number of non-isomorphic groups of order 10 = ?

in Set Theory & Algebra by Active (5k points) | 70 views
Ans will be 4, with lagrange theorem

srestha  mam how ...

How langrage theorem applied here ??

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

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:-

Please log in or register to answer this question.

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
50,737 questions
57,313 answers
105,051 users