[GAP Forum] special bijective maps on right loops

[Chris Wensley]

Dear Akhilesh Yadav

This is not an attempt to answer your question, but just a comment on the terminology.
Groupoids in GAP are categories in which every morphism is invertible (see package Gpd).  The term 'groupoid' has also been used in mathematics to denote a set with a binary operation.  Such structures in GAP use the other commonly used term, namely 'magma'.

Best wishes, Chris Wensley
________________________________________
From: forum-bounces at gap-system.org <forum-bounces at gap-system.org> on behalf of Akhilesh Yadav <akhileshyadav538 at gmail.com>
Sent: 14 July 2015 17:49
To: forum at gap-system.org
Subject: [GAP Forum] special bijective maps on right loops

I asked a question on gap forum for calculating some special maps. But I
realized that it was not properly written. So I apologize to you.
I am again asking the same question:

A groupoid (S, o) with identity e is called a right loop if for every $x, y
$ in S, the equation $Xox = y$  has a unique solution in  S.
A right loop $(S, o)$ is called a right loop with unique inverses if for
each x in S there exists a unique element $x^{\prime}$ (we call inverse of
x) in S such that $x o x^{\prime} = e = x^{\prime} o x$.


Suppose that (S, o) is a right loop with unique inverses.  Then our
question is:
How to calculate bijective maps f on right loop S such that f(e)= e and
$f(x o y) = [f(x^{\prime})]^{\prime} o f(y)$ ?
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