# Group Theory - Group of Even Order

Modern Algebra

Group Theory (XXII)

Group of Even Order

If G is a group of even order, prove it has an element a which is not equal to e satisfying a^2 = e.

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Modern Algebra

Group Theory (XXII)

Group of Even Order

By:- Thokchom Sarojkumar Sinha

If is a group of even order, prove it has an element satisfying .

Proof:- Let be a group of even order.

We have to ...

#### Solution Summary

It is proven that if G is a group of even order, it has an element a which is not equal to e satisfying a^2 = e. The solution is detailed and well presented.