Verbally closed subgroups of free groups
A. Myasnikov, V. Roman'kov
TL;DR
This paper proves that in free groups of finite rank, any subgroup that is verbally closed must also be a retract, revealing a structural property of these subgroups.
Contribution
It establishes that verbally closed subgroups of free groups are precisely the retracts, providing a new characterization of these subgroups.
Findings
Verbal closure implies retraction in free groups.
Every verbally closed subgroup of a finite rank free group is a retract.
The result clarifies the structure of subgroups in free groups.
Abstract
We prove that every verbally closed subgroup of a free group of a finite rank is a retract of
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Finite Group Theory Research