Two results about the hypercube

Two Results about Fixed Point of Multifunctions

Two Results about Finite Groups

I would like to discuss two results about finite groups: (0) All finite groups of odd order are solvable. (F) A finite group is nilpotent if it admits a fixed point free automorphism of prime order. Walter Feit and I proved (0) after a prolonged joint effort [5]. A critical special case of (0) was proved by Walter Feit, Marshall Hall, Jr. and me [4]. A slightly stronger result than (F) is in th...

On Two Results about Fibrations

Let h., denote a reduced homology theory on the category of based spaces and let h, denote the corresponding extension to an unreduced homology theory on the category of unbased spaces given by h , ( X ) = h,(X+), where X+ denotes X with the addition of a disjoint basepoint. The following was proved by W. Chach61ski [2], using the elaborate machinery of 'cellular inequalities' developed by E. D...

Two Results about Quantum Messages

The comparison of communication protocols using quantum messages with protocols using classical messages is a central topic in information and communication theory. It is always good to understand such questions well in the simplest settings where they arise. An example is the setting of one-way communication complexity, which is rich enough to lead to many interesting questions, yet accessible...

two results about fixed point of multifunctions