Conjugation of injections by permutations

Details Conjugation of injections by permutations Conjugation of injections by permutations

2010-03-10

arxiv.org/abs/1003.2027v1

Semigroup Forum, Volume 81, (2010) 297-324

Mathematics

Group Theory

27 pages, 4 figures

Scientific paper

10.1007/s00233-010-9224-3

Let X be a countably infinite set, and let f, g, and h be any three injective self-maps of X, each having at least one infinite cycle. (For instance, this holds if f, g, and h are not bijections.) We show that there are permutations a and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We also prove a version of this statement that holds for infinite sets X that are not necessarily countable. This generalizes results of Droste and Ore about permutations.

Affiliated with

Also associated with

No associations

Rating

Conjugation of injections by permutations 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 Conjugation of injections by permutations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conjugation of injections by permutations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-341392