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Groups : Indentities and Inverses

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If G is a group, then

(1) the identity element of G is unique,
(2) every a belongs to G has a unique inverse in G.

© BrainMass Inc. brainmass.com September 21, 2018, 3:51 am ad1c9bdddf - https://brainmass.com/math/group-theory/groups-identities-inverses-102083

Solution Preview

Proof:

(1) Suppose that e and e' are both identity elements in G. Then, by group property (2), we have

ea= a , for every a in G.

In particular, ee' = ...

Solution Summary

Identities and inverses are discussed. The expert identifies the elements of G for a group.

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