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## Number of non-isomorphic groups of order 10 = ?

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Ans will be 4, with lagrange theorem
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srestha  mam how ...

How langrage theorem applied here ??

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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
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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

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