Frobenius reciprocity is the natural isomorphism 
for a subgroup 
. Thus induction of representations
is left adjoint to restriction.
Frobenius Reciprocity
See also
Group Representation, SubgroupExplore with Wolfram|Alpha
References
Serre, J.-P. Linear Representations of Finite Groups. New York: Springer-Verlag, 1977.Cite this as:
Weisstein, Eric W. "Frobenius Reciprocity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FrobeniusReciprocity.html