INDICABLE GROUPS AND ENDOMORPHIC PRESENTATIONS
نویسندگان
چکیده
منابع مشابه
Endomorphic Presentations of Branch Groups
We introduce “endomorphic presentations”, or L-presentations: group presentations whose relations are iterated under a set of substitutions on the generating set, and show that a broad class of groups acting on rooted trees admit explicitly constructible finite L-presentations, generalising results by Igor Lysionok and Said Sidki.
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We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent subgroup of G, then a left-invariant total order on G can be chosen so that its restriction to H is both left-invariant and right-invariant. Both results fo...
متن کاملL-presentations and Branch Groups
We introduce L-presentations: group presentations endowed with a set of substitutions on the generating set, and show that a broad class of groups acting on rooted trees admit explicitly constructible finite L-presentations.
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Using elementary ideas from formal language theory we introduce a kind of group presentation which makes solution of the word problem easy in the case of a nite group, and which in that case also makes possible an eecient algorithm to compute a traversal, i.e., a list of strings in generators in which each group element occurs exactly once.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2011
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089511000632