1. Let G be a finite group with an even number of elements. Show that there must be some element a in G, ae (e the identity element) such that a² = e.
1. Let G be a finite group with an even number of elements. Show that there must be some element a in G, ae (e the identity element) such that a² = e.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 15E: 15. Assume that can be written as the direct sum , where is a cyclic group of order .
Prove that...
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