Bulitko's Lemma for acylindrical splittings

TL;DR

This paper extends Bulitko's Lemma to equations over groups with $$-acylindrical splittings, broadening its applicability in group theory.

Contribution

The paper introduces a generalization of Bulitko's Lemma applicable to groups with $$-acylindrical splittings, enhancing theoretical tools for group equations.

Findings

Generalization of Bulitko's Lemma to $$-acylindrical splittings

Applicable to equations over groups with specific splittings

Provides new methods for analyzing group homomorphisms

Abstract

We generalize Bulitko's Lemma to equations over (or homomorphisms into) groups that have $\kappa$-acylindrical splittings.