Suppose that G is an Abelian group with an odd number of elements. show that the product of all the elements of G is the identity. Let |G|=8. Show that G must have and element of order 2.
Follow Math Help Forum on Facebook and Google+
Originally Posted by Juancd08 Suppose that G is an Abelian group with an odd number of elements. show that the product of all the elements of G is the identity. Hint: Pair and so that . Note why you need the fact that is odd. Let |G|=8. Show that G must have and element of order 2. Let and construct . By Lagrange's theorem . Since this is a cyclic group and 2 divides its order we can find an element of that order.
View Tag Cloud