Idempotent endomorphisms of a graph
نویسندگان
چکیده
منابع مشابه
Fixed points of endomorphisms of graph groups
It is shown, for a given graph group G, that the fixed point subgroup Fix' is finitely generated for every endomorphism ' of G if and only if G is a free product of free abelian groups. The same conditions hold for the subgroup of periodic points. Similar results are obtained for automorphisms if the dependence graph of G is a transitive forest.
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Let X be a finite set. We denote by T (X) the monoid of all (total) transformations on X and by Sym(X) the symmetric group on X. An element a 2 T (X) \ Sym(X) is said to be singular. In 1966 Howie [4] proved that every singular transformation a 2 T (X) can be expressed as a product of idempotents of T (X). This result was generalized by Fountain and Lewin [2] for the case of independence algebr...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00105-9