Search results for "free product"
showing 8 items of 8 documents
Highly transitive actions of groups acting on trees
2015
We show that a group acting on a non-trivial tree with finite edge stabilizers and icc vertex stabilizers admits a faithful and highly transitive action on an infinite countable set. This result is actually true for infinite vertex stabilizers and some more general, finite of infinite, edge stabilizers that we call highly core-free. We study the notion of highly core-free subgroups and give some examples. In the case of amalgamated free products over highly core-free subgroups and HNN extensions with highly core-free base groups we obtain a genericity result for faithful and highly transitive actions. In particular, we recover the result of D. Kitroser stating that the fundamental group of …
Homogeneous actions on the random graph
2018
We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite.
Highly transitive actions of free products
2013
We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group $\PSL_2(\Z)\simeq (\Z/2\Z)*(\Z/3\Z)$ admits a faithful and highly transitive action on a countable set.
Sourdough and cereal-based foods: traditional and innovative products
2017
Cereals represent the main crop of the five continents and contribute greatly to the diet of several populations. Cereals often undergo a fermentation before eating. This process is fundamental to confer high sensory quality, as well as to preserve and enhance the nutritional and safety aspects of the resulting products. Fermented cereal based foods are complex microbial ecosystems, mainly represented by lactic acid bacteria and yeasts. Among these products, sourdough is worldwide applied to produce breads. Sourdough technology is also used to improve the final characteristics of fortified and gluten–free breads. This chapter focuses on the use of cereals to produce the most relevant fermen…
Some algebraic and topological properties of the nonabelian tensor product
2013
Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.
CODING PARTITIONS OF REGULAR SETS
2009
A coding partition of a set of words partitions this set into classes such that whenever a sequence, of minimal length, has two distinct factorizations, the words of these factorizations belong to the same class. The canonical coding partition is the finest coding partition that partitions the set of words in at most one unambiguous class and other classes that localize the ambiguities in the factorizations of finite sequences. We prove that the canonical coding partition of a regular set contains a finite number of regular classes and we give an algorithm for computing this partition. From this we derive a canonical decomposition of a regular monoid into a free product of finitely many re…
Counterexamples to the Kneser conjecture in dimension four.
1995
We construct a connected closed orientable smooth four-manifold whose fundamental group is the free product of two non-trivial groups such that it is not homotopy equivalent toM 0#M 1 unlessM 0 orM 1 is homeomorphic toS 4. LetN be the nucleus of the minimal elliptic Enrique surfaceV 1(2, 2) and putM=N∪ ∂NN. The fundamental group ofM splits as ℤ/2 * ℤ/2. We prove thatM#k(S 2×S2) is diffeomorphic toM 0#M 1 for non-simply connected closed smooth four-manifoldsM 0 andM 1 if and only ifk≥8. On the other hand we show thatM is homeomorphic toM 0#M 1 for closed topological four-manifoldsM 0 andM 1 withπ 1(Mi)=ℤ/2.
On the Toeplitz algebras of right-angled and finite-type Artin groups
1999
The graph product of a family of groups lies somewhere between their direct and free products, with the graph determining which pairs of groups commute and which do not. We show that the graph product of quasi-lattice ordered groups is quasi-lattice ordered, and, when the underlying groups are amenable, that it satisfies Nica's amenability condition for quasi-lattice orders. As a consequence the Toeplitz algebras of these groups are universal for covariant isometric representations on Hilbert space, and their representations are faithful if the isometries satisfy a properness condition given by Laca and Raeburn. An application of this to right-angled Artin groups gives a uniqueness theorem …