The Howie conjecture asks whether every finite nonsingular system of group equations over a group 
has a solution in some overgroup containing
. For 
equations in 
unknowns, nonsingularity means that the 
integer exponent-sum matrix has row matrix rank 
over 
, so 
. The group 
is arbitrary and may have torsion.
Howie Conjecture
See also
Group Equation, Kervaire Conjecture, Matrix Rank, Normal ClosureExplore with Wolfram|Alpha
References
Klyachko, A. and Thom, A. "New Topological Methods to Solve Equations over Groups." Algebr. Geom. Topol. 17, 331-353, 2017. https://doi.org/10.2140/agt.2017.17.331.Cite this as:
Weisstein, Eric W. "Howie Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HowieConjecture.html