has an inverse. Show that if ax = ay, then x = y.
with an = e (Hint: Consider the set {e, a, a2 , …, am }, where m is
the number of elements of G and use cancellation. (problem 5))
Mathematics Homework Solutions
#60256
Algebraic Structures, Inverses, Finite Group, Identity
5. Let (A, *) be an algebraic structure, and suppose that A is associative, has an identity, e, and that a Є A has an inverse. Show that if ax = ay, then x = y.
8. Let G be a finite group with identity e, and let . Show that there is an n Є N with a^n = e (Hint: Consider the set {e, a, a2 , …, am }, where m is the number of elements of G and use cancellation. (problem 5))
Algebraic Structures, Inverses, Finite Group, Identity are investigated.
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