Some characterizations of Howson PC-groups
Jordi Delgado
TL;DR
This paper explores properties of Howson PC-groups, establishing their equivalence with being fully residually free and free products of free-abelian groups within partially commutative groups.
Contribution
It proves the equivalence of key algebraic properties in the class of partially commutative groups, clarifying their structural relationships.
Findings
Being Howson is equivalent to being fully residually free in PC-groups.
Such groups are also characterized as free products of free-abelian groups.
These conditions are shown to be equivalent within the class.
Abstract
We show that in the class of partially commutative groups, the conditions of being Howson, being fully residually free, and being free product of free-abelian groups, are equivalent.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Topology and Set Theory · semigroups and automata theory