# [GAP Forum] RE: ? trouble getting started ?

Brian Beckman brianbec at comcast.net
Sun Jul 25 19:02:52 BST 2004

```I was able to induce from the example that A*B does not mean first apply A,
then apply B, then apply A-inverse, or, in conjugation notation, (A ^ B) ^
(A ^ -1).  This looked promising at first, since
(1,2)*(1,2,3)=((1,2)^(1,2,3))^((1,2)^-1); --> true but ... ooops
(1,2,3)*(1,2)=((1,2,3)^(1,2))^((1,2,3)^-1); did not work out.

sorry to 'blog' like this. If this is forum abuse just tell me and I will
stop.

_____

From: Brian Beckman [mailto:brianbec at comcast.net]
Sent: Sunday, July 25, 2004 10:44 AM
To: forum at mail.gap-system.org
Cc: brianbec at comcast.net
Subject: ? trouble getting started ?

Hello --

I had some trouble understanding Permutations as presented in the tutorial
and I wondered whether someone might help me out.

I'm working through
http://www.gap-system.org/Manuals/doc/htm/tut/CHAP002.htm#SECT008 .  I was
able to understand "conjugating" permutations with the "caret" operator, so,
for instance, (1,2)^(1,2,3)=(2,3); made sense to me and
(1,2,3)^(1,2)=(1,3,2); also made sense.  I could not figure out
"multiplication" of purmutations, however, so (1,2)*(1,2,3)=(1,3); did not
make sense to me and (1,2,3)*(1,2)=(2,3); did not make sense. I expected
(1,2)*(1,2,3)=(1,2,3)^(1,2) and (1,2,3)*(1,2)=(1,2)^(1,2,3), but that's
obviously not the case.

I apologize for my ignorance of the subject, but I am attempting to use GAP
to learn algebra.  So far, I only know of one kind of operation for
permutations (that being composition or conjugation) and I couldn't quickly
figure out what your multiplication means. I'll continue to play around with
it and may possibly find my own answer, but it's humiliating to get
frustrated by the very first algebraic operation I attempted here.

Regards,
Brian Beckman

```