Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups

Details Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups

2010-12-11

arxiv.org/abs/1012.2480v2

Mathematics

Group Theory

30 pages

Scientific paper

Let $G$ be an almost simple group. We prove that if $x \in G$ has prime order $p \ge 5$, then there exists an involution $y$ such that $$ is not solvable. Also, if $x$ is an involution then there exist three conjugates of $x$ that generate a nonsolvable group, unless $x$ belongs to a short list of exceptions, which are described explicitly. We also prove that if $x$ has order $6$ or $9$, then there exists two conjugates that generate a nonsolvable group.

Affiliated with

Also associated with

No associations

Rating

Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable 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 Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-105808