Mathematics – Group Theory
Scientific paper
2010-11-09
Mathematics
Group Theory
42 pages
Scientific paper
We construct an extension $E(A,G)$ of a given group $G$ by infinite non-Archimedean words over an discretely ordered abelian group like $Z^n$. This yields an effective and uniform method to study various groups that "behave like $G$". We show that the Word Problem for f.g. subgroups in the extension is decidable if and only if and only if the Cyclic Membership Problem in $G$ is decidable. The present paper embeds the partial monoid of infinite words as defined by Myasnikov, Remeslennikov, and Serbin (Contemp. Math., Amer. Math. Soc., 378:37-77, 2005) into $E(A,G)$. Moreover, we define the extension group $E(A,G)$ for arbitrary groups $G$ and not only for free groups as done in previous work. We show some structural results about the group (existence and type of torsion elements, generation by elements of order 2) and we show that some interesting HNN extensions of $G$ embed naturally in the larger group $E(A,G)$.
Diekert Volker
Myasnikov Alexei
No associations
LandOfFree
Group extensions over infinite words 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 Group extensions over infinite words, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Group extensions over infinite words will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-493046