On the WGSC Property in Some Classes of Groups

Otera, Daniele Ettore; Russo, Francesco G.

doi:10.1007/s00009-009-0021-8

Cited by 11 publications

(4 citation statements)

References 12 publications

(22 reference statements)

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“…An example comes from an asymptotic invariant of discrete groups (i.e. a well-defined property of groups which is invariant under quasi-isometries [8,13]) of topological nature, due to Brick and Mihalik [2,18]. Definition 2.8 (See [2,18]).…”

Section: Resultsmentioning

confidence: 99%

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Otera¹,

Russo²,

Tanasi³

2013

Bulletin of the Korean Mathematical Society

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Section: Resultsmentioning

confidence: 99%

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Otera¹,

Russo²,

Tanasi³

2013

Bulletin of the Korean Mathematical Society

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“…Although this proof is very short, it relies on other deep results. First of all in [43] it is proved that almost-convex groups are tame 1-combable (see the next section for definitions and more details) and hence qsf by [32]. By the main result of [44], one can infer that such a group admits an easy wgsc-representation with an additional finiteness condition.…”

Section: Almost-convex Groupsmentioning

confidence: 97%

“…Remark 3.2. Another proof of a slightly weaker form of Proposition 1 can be deduced from the recent papers [43,44]. Although this proof is very short, it relies on other deep results.…”

Section: Almost-convex Groupsmentioning

confidence: 99%

Topics in Geometric Group Theory. Part I

Otera¹,

Poénaru²

2018

Preprint

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This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (qsf), geometric simple connectivity (gsc), topological inverse-representations, and the notion of easy groups. As we will explain, these properties are central in the theory of discrete groups seen from a topological viewpoint at infinity. Also, we shall outline the main steps of the achievements obtained in the last years around the very general question whether or not all finitely presented groups satisfy these conditions.

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“…For instance, the Baumsalg-Solitar groups are classical generalizations (see [3,12] but also [29,32] for similar semidirect products). A way to construct them is the following.…”

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confidence: 99%

Some considerations on Hydra groups and a new bound for the length of words

Otera

Russo

2014

Mathematica Slovaca

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ABSTRACT. After a survey on some recent results of Riley and others on Ackermann functions and Hydra groups, we make an analogy between DNA sequences, whose growth is the same of that of Hydra groups, and a musical piece, written with the same algorithmic criterion. This is mainly an aesthetic observation, which emphasizes the importance of the combinatorics of words in two different contexts. A result of specific mathematical interest is placed at the end, where we sharpen some previous bounds on deterministic finite automata in which there are languages with hairpins. Hydra groupsThe combinatorics of words is increased significatively in the last years, since it is a powerful tool for the description of several processes in pure and applied sciences. A classic reference on the topic is [24] and will be used for the basic notions. We recall that a nonempty set A (which will be always assumed to be finite) is said to be an alphabet and its elements are called letters. By A + we denote the free semigroup generated by A, i.e. the set of all finite sequences of letters with the operation of concatenation. Elements of A + will be called words. It is well known that each word can be written in a unique way as a sequence of letters, so it is possible to define for each word w its length |w|:It is useful (though not necessary) to introduce the formal empty word ε: that is a word of length 0 such that2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 57M50; Secondary 68R05, 68Q15. K e y w o r d s: isoperimetric functions, finitely presented groups, lengths of words, counterpoint, Myhill-Nerode's theorem.

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On the WGSC Property in Some Classes of Groups

Cited by 11 publications

References 12 publications

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Topics in Geometric Group Theory. Part I

Some considerations on Hydra groups and a new bound for the length of words

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