2,077 research outputs found
Automatic Quotients of Free Groups
Automatic groups admitting prefix closed automatic structures with uniqueness
are characterized as the quotients of free groups by normal subgroups
possessing sets of free generators satisfying certain language-theoretic
conditions.Comment: 14 pages, no figures. Minor corrections. Statements of theorems and
lemmas are unchange
Groups whose word problems are not semilinear
Suppose that G is a finitely generated group and W is the formal language of
words defining the identity in G. We prove that if G is a nilpotent group, the
fundamental group of a finite volume hyperbolic three-manifold, or a
right-angled Artin group whose graph lies in a certain infinite class, then W
is not a multiple context free language
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