Show that if every element in a group is its own inverse, then the group must be abelian.

0

18kviews

Show that if every element in a group is its own inverse, then the group must be abelian.

written 7.3 years ago by

teamques10 ★ 64k

modified 2.2 years ago by

pedsangini276 • 4.7k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: Dec 2013

discrete mathematics

ADD COMMENT EDIT

1 Answer

1

1.8kviews

written 7.3 years ago by

teamques10 ★ 64k

Let a, b ∈ G.

So we have $a^{-1} = a$ and $b^{-1} = b$.

Also a • b ∈ G, therefore $a • b = (a.b)^{-1}= b^{-1} • a^{-1} = b • a$.

So we have a • b = b • a,

Hence, G is abelian.

ADD COMMENT EDIT

Please log in to add an answer.