An Aschbacher--O'Nan--Scott theorem for countable linear groups

Details An Aschbacher--O'Nan--Scott theorem for countable linear groups An Aschbacher--O'Nan--Scott theorem for countable linear groups

2009-11-03

arxiv.org/abs/0911.0628v2

Mathematics

Group Theory

8 pages

Scientific paper

The purpose of this note is to extend the classical Aschbacher--O'Nan--Scott theorem for finite groups to the class of countable linear groups. This relies on the analysis of primitive actions carried out in a previous paper. Unlike the situation for finite groups, we show here that the number of primitive actions depends on the type: linear groups of almost simple type admit infinitely (and in fact unaccountably) many primitive actions, while affine and diagonal groups admit only one. The abundance of primitive permutation representations is particularly interesting for rigid groups such as simple and arithmetic ones.

Affiliated with

Also associated with

No associations

Rating

An Aschbacher--O'Nan--Scott theorem for countable linear groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An Aschbacher--O'Nan--Scott theorem for countable linear groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Aschbacher--O'Nan--Scott theorem for countable linear groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-618679