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Number of non-isomorphic groups of order 10 = ?

in Set Theory & Algebra 129 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:-

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