Determine the number of saddle points under specified conditions February 13

Suppose a function with two variables $f(x, y)$ is smooth enough everywhere. If it has a local minimum and a local maximum, can we say that there are at least two saddle points as well? If so, how can we prove it? If not, then under what conditions s

Group of order $p^nq^m$ February 13

Let $G$ be a semi-direct product of a finite $p$-group and a finite $q$-group where $p$ and $q$ are prime numbers. We know that $G$ is soluble and every normal minimal of $G$ is elementary abelian. If $G$ does not contain a normal minimal subgroup of

Solvable group of order $p^nq^m$ February 13

Let $G$ be a semi-direct product of a $p$-group and a $q$-group where $p$ and $q$ are prime number. If $G$ does not contain a normal minimal subgroup of order $q$ what we can say about $q$-sylow of $G$? For example is it cyclic?

What is the saddle-point approximation February 13

I want to take advice which books are useful to understand saddle point approximation. Can you give suggestion about that ?Also, if you explain what is the saddle point approximation, I will be so happy :)Thank you so much.

the Frattini subgroup of some solvable groups February 13

have been looking for information about Frattini subgroup of a finite group of order p^3q and p^n q for distinct prime p and q?