Mathematics – Logic
Scientific paper
2001-12-22
Mathematics
Logic
Scientific paper
In this paper we mainly consider the class LN of all locally nilpotent groups. We first show that there is no universal group in LN_lambda if lambda is a cardinal such that lambda = lambda^{aleph_0}; here we call a group G universal (in LN_lambda) if any group H in LN_lambda can be embedded into G where LN_lambda denotes the class of all locally nilpotent groups of cardinality at most lambda. However, our main interest is the construction of torsion-free epi-universal groups in LN_lambda, where G in LN_lambda is said to be epi-universal if any group H in LN_lambda is an epimorphic image of G. Thus we give an affirmative answer to a question by Plotkin. To prove the torsion-freeness of the constructed locally nilpotent group we adjust the well-known commutator collecting process due to P. Hall to our situation. Finally, we briefly discuss how to use the same methods as for the class LN for other canonical classes of groups to construct epi-universal objects.
Göbel Rüdiger
Shelah Saharon
Wallutis Simone
No associations
LandOfFree
On universal and epi-universal locally nilpotent 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 On universal and epi-universal locally nilpotent groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On universal and epi-universal locally nilpotent groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-50194