Displaying similar documents to “The Dehn functions of O u t ( F n ) and A u t ( F n ) ”

Systolic invariants of groups and 2 -complexes via Grushko decomposition

Yuli B. Rudyak, Stéphane Sabourau (2008)

Annales de l’institut Fourier

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We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of  2 -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all 2 -complexes with unfree fundamental group that improves the previously known bounds...

A note on intersection dimensions of graph classes

Petr Hliněný, Aleš Kuběna (1995)

Commentationes Mathematicae Universitatis Carolinae

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The intersection dimension of a graph G with respect to a class 𝒜 of graphs is the minimum k such that G is the intersection of some k graphs on the vertex set V ( G ) belonging to 𝒜 . In this paper we follow [ Kratochv’ıl J., Tuza Z.: , Graphs and Combinatorics 10 (1994), 159–168 ] and show that for some pairs of graph classes 𝒜 , ℬ the intersection dimension of graphs from ℬ with respect to 𝒜 is unbounded.

On strongly sum-free subsets of abelian groups

Tomasz Łuczak, Tomasz Schoen (1996)

Colloquium Mathematicae

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In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists n 0 = n 0 ( l ) with the following property: for every n ≥ n 0 and any n elements a 1 , . . . , a n of a group such that the product of any two of them is different from the unit element of the group, there exist l of the a i such that a i j a i k ≠ a m for 1 ≤ j < k ≤ l and 1 ≤ m ≤ n . In this note we answer this question in the affirmative in the first non-trivial case when l=3 and the group is abelian, proving the following result.

Whitney blocks in the hyperspace of a finite graph

Alejandro Illanes (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a finite graph. Let C ( X ) be the hyperspace of all nonempty subcontinua of X and let μ : C ( X ) → ℝ be a Whitney map. We prove that there exist numbers 0 < T 0 < T 1 < T 2 < ⋯ < T M = μ ( X ) such that if T ∈ ( T i - 1 , T i ) , then the Whitney block μ - 1 ( T i - 1 , T i ) is homeomorphic to the product μ - 1 ( T ) × ( T i - 1 , T i ) . We also show that there exists only a finite number of topologically different Whitney levels for C ( X ) .