perplexus.info :: Just Math : Commutative Group 2

Commutative Group 2 (Posted on 2023-02-26)

A certain group is known to have the property that every element is its own inverse.

Prove that the group is commutative.

Submitted by Brian Smith

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Solution: (Hide)

My solution is below. Steven Lord provides another solution here.

Let the group operator be denoted as @. Let A and B be two arbitrary elements of the group and I be the identity.

A@B@A@B = A@B@A@B
A@(B@A)@B = (A@B)@(A@B)
A@(B@A)@B = I
A@A@(B@A)@B@B = A@I@B
I@(B@A)@I = A@B
B@A = A@B

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	Tommie Marshall	2023-04-01 03:05:57
possible solution	Steven Lord	2023-02-26 09:38:32

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