A 1 1/2-dimensional version of Hopf's Theorem on the number of ends of a group.
Using Lipschitz distance on Outer space we give another proof of the train track theorem.
We show that the termination of Mohri's algorithm is decidable for polynomially ambiguous weighted finite automata over the tropical semiring which gives a partial answer to a question by Mohri [29]. The proof relies on an improvement of the notion of the twins property and a Burnside type characterization for the finiteness of the set of states produced by Mohri's algorithm.
We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.
The order of every finite group can be expressed as a product of coprime positive integers such that is a connected component of the prime graph of . The integers are called the order components of . Some non-abelian simple groups are known to be uniquely determined by their order components. As the main result of this paper, we show that the projective symplectic groups where are also uniquely determined by their order components. As corollaries of this result, the validities of a...