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I would like to know whether the problem described below has appeared in the literature and/or whether similar questions have been studied. I would be very happy to find some references or, if none ...

Context: Algorithms to find short paths on Cayley graphs of (finite) groups are of some interest - see below. There can be several approaches to that task. One of ideas coming to my mind - in some ...

Let $D_{n}$ denotes the dihedral group of order $2n$. Firstly, for self-referencing of the question, I give some definitions which are standard. Let $G$ be a finite group. A subset $S$ of group $G$ ...

We consider a group finite $G$. We say a set $A\subset G$ injects a set $B$ if $|A+B| = |A||B|$, and let $I(B) = \max \{|A| :A\text{ injects } B\}$. For a subgroup $H$, it is well-known that $I(H) = |...