Talk:SQ-universal group

Definition
The original definition of SQ-universality that appeared on this page was incorrect and was in fact the definion of SQ-universality for the class of finite groups. Bernard Hurley 00:05, 23 September 2006 (UTC)

Examples
I'd like to request some examples added to this article. For example, I beleive that SL(2,Z) is SQ-universal, since it has the the free group in two generators as a subgroup. Since its isomorphic to the braid group B_3, and all other higher braid groups B_n have B_3 as a subgroup, that implies all braid groups (except the trivial B_1 and the B_2=Z) are SQ universal. Right? Ditto for mapping class group.


 * The argument you give for braid and mapping class groups are not correct: containing a SQ-universal group does not imply SQ-universality (think of a simple group). This is OK for SL(2,Z) though since it is virtually free. 82.234.76.19 (talk) 05:47, 24 March 2010 (UTC)

Less clear to me is when a monodromy might be SQ-universal; but given the close relationship to braids and mapping classes, I'd think some general statements should be possible.. linas 22:53, 6 April 2007 (UTC)

what SQ stays for?
Any idea why it is SQ-universal?--Tosha (talk) 01:50, 31 March 2010 (UTC)


 * S = subgroup, Q = quotient. --Zundark (talk) 11:59, 16 August 2011 (UTC)