Howie's conjecture: every nonsingular system of equations over a group is solvable in an overgroup

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This event attributed to Unreleased internal OpenAI model

Claims Theorem 1: for every group $G$ and every finite system $w_1,\dots,w_m\in G*F_n$ whose exponent-sum matrix has rank $m$ over $\mathbb Q$, the canonical map $G\to(G*F_n)/\langle\langle w_1,\dots,w_m\rangle\rangle$ is injective, so the system has a simultaneous solution in an overgroup. This contains the Kervaire-Laudenbach conjecture (one equation, one unknown, nonzero exponent sum) and the Kervaire conjecture. It does NOT control the overgroup (no finiteness, solvability or other structure of the solution group), and says nothing about singular systems. parent of this event

Lean (companion, one unimodular relator only): Kervaire solution module evidence for this event

Howie's conjecture: every nonsingular system of equations over a group is solvable in an overgroup parent of this event

Howie's conjecture: every nonsingular system of equations over a group is solvable in an overgroup evidence for this event

VibeMathed record: Howie's conjecture: every nonsingular system of equations over a group is solvable in an overgroup evidence for this event

Howie (1981), On pairs of 2-complexes and systems of equations over groups evidence for this event

Companion: The Kervaire theorem for groups evidence for this event