In mathematics, the Fréchet derivative is a derivative defined on Banach spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued function of multiple real variables, and to define the functional derivative used widely in the calculus of variations.
Generally, it extends the idea of the derivative from real-valued functions of one real variable to functions on Banach spaces. The Fréchet derivative should be contrasted to the more general Gâteaux derivative which is a generalization of...
Suppose $H$ is a subgroup of a group $G$, where $|H|=p$, for $p$ a prime. I need to describe, up to isomorphism, all possible quotient groups $F/N$, where $ N \trianglelefteq G$ and $N \leqslant F \leqslant \langle H, N \rangle$.
Here is my attempt thus far - note that it includes a lot of subc...
