For any group G and any finite system of m equations in n unknowns, with 1≤m≤n, if the exponent-sum matrix has row rank m over the rationals, then G embeds in the group formed by adjoining the unknowns and imposing the equations.
For any group G and any finite system of m equations in n unknowns, with 1≤m≤n, if the exponent-sum matrix has row rank m over the rationals, then G embeds in the group formed by adjoining the unknowns and imposing the equations. Thus the system has a simultaneous solution in an overgroup.
For any group G and any finite system of m equations in n unknowns, with 1≤m≤n, if the exponent-sum matrix has row rank m over the rationals, then G embeds in the group formed by adjoining the unknowns and imposing the equations. Thus the system has a simultaneous solution in an overgroup.
If correct, resolves Howie’s conjecture for every coefficient group and finite nonsingular system.
Does every finite nonsingular system of equations over an arbitrary group have a simultaneous overgroup solution?
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OpenAI reports a solution to Howie’s nonsingular-systems conjecture
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