# Normal subgroups and product of two right cosets

Modern Algebra

Group Theory (XXXV)

Cosets of Subgroups of a Group

Normal Subgroups of a Group

A subgroup N of G is a normal subgroup of G if and only if the product of two right cosets of N in G is again a right coset of N in G.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:49 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/normal-subgroups-product-two-right-cosets-63784

#### Solution Preview

The solution of the Posting is in the attached file.

Thanks for using BrainMass.com. Have a great day.

Modern Algebra

Group Theory (XXXV)

Cosets of Subgroups of a Group

Normal Subgroups of a Group

By:- Thokchom Sarojkumar Sinha

A subgroup of is a normal subgroup of if and only if the product of two right cosets of in

is again a right coset of in .

...

#### Solution Summary

This solution is comprised of a detailed explanation to prove the statement "A subgroup N of G is a normal subgroup of G if and only if the product of two right cosets of N in G is again a right coset of N in G". The solution is detailed and well presented.