Let a group 
have a group presentation
 |
so that 
,
where 
is the free group with basis 
and 
is the normal subgroup
generated by the 
.
If 
is a group with 
and if 
for all 
, then there is a surjective homomorphism 
with 
for all 
.
von Dyck's Theorem
See also
Dyck's Theorem, Free Group, Normal SubgroupExplore with Wolfram|Alpha
References
Rotman, J. J. An Introduction to the Theory of Groups, 4th ed. New York: Springer-Verlag, p. 346, 1995.Referenced on Wolfram|Alpha
von Dyck's TheoremCite this as:
Weisstein, Eric W. "von Dyck's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/vonDycksTheorem.html