1
$\begingroup$

Dear all,

According to the notation of Wilson's book "The finite simple groups" ( books.google.com/books?isbn=1848009879, page 9) $ A_{.} B $ denotes an unspecified extension. Now, I want to know what does "unspecified extension of $A$ and $B$" mean?

$\endgroup$
  • $\begingroup$ First you must type your question correctly. Also read the notatio 1.6 in page 24 of the book! $\endgroup$ – majid arezoomand Jan 6 '13 at 6:57
  • $\begingroup$ @ majid arezoomand i am so sorry, but actually you have repeated my question! $\endgroup$ – sebastian Jan 6 '13 at 7:25
  • $\begingroup$ I assume "unspecified" here just means "arbitrary". But as Derek Holt points out the notation used is now fairly standard if the dot is placed correctly, including the convention about which group is the quotient but allowing for the extension to be nonsplit. $\endgroup$ – Jim Humphreys Jan 6 '13 at 23:49
8
$\begingroup$

I don't have the book at hand, but I think the usual meaning of $G = A.B$ for groups $A$ and $B$ is that $G$ has a normal subgroup isomorphic to $A$ such that the quotient $G/A$ is isomorphic to $B$. Some authors only write non-split extensions in this way, but if the book states that $A.B$ denotes an "unspecified" extension, this means that it may be split or not.

$\endgroup$
  • 9
    $\begingroup$ The ATLAS convention, which I think is followed by Wilson, is to specify an extension that is known to be nonsplit by $A^\cdot B$ (with a raised dot, which I am not managing to reproduce accurately here). Also $A:B$ denotes a split extension, and $A.B$ one which may or may not be split. $\endgroup$ – Derek Holt Jan 6 '13 at 14:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.