Finite automata for Schreier graphs of virtually free groups
نویسندگان
چکیده
منابع مشابه
Finite automata for Schreier graphs of virtually free groups
The Stallings construction for f.g. subgroups of free groups is generalized by introducing the concept of Stallings section, which allows an efficient computation of the core of a Schreier graph based on edge folding. It is proved that those groups admitting Stallings sections are precisely f.g. virtually free groups, through a constructive approach based on Basse-Serre theory. Complexity issue...
متن کاملFurstenberg Entropy Realizations for Virtually Free Groups and Lamplighter Groups
Let (G, μ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε > 0 such that the Furstenberg entropy of any (G, μ)-stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This co...
متن کاملLifts, derandomization, and diameters of Schreier graphs of Mealy automata
It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and present a class of automata for which the same is true. However, we also show that some automata in this class do not give rise to expander graphs.
متن کاملA Characterisation of Virtually Free Groups
We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.
متن کاملOn Laplacian energy of non-commuting graphs of finite groups
Let $G$ be a finite non-abelian group with center $Z(G)$. The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$. In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups..
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2016
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgth-2015-0028