I am having no knowledge of GAP but I want some calculations in group algebra $FG=F_pD_{2n}$. Here $F_p$ is a finite field with $p$ elements and $D_{2n}=\{a, b\mid a^n, b^2, (ab)^2=1\}$ is Dihedral group. How to do calculations in GAP. For example if I want to find inverse of say $2+a^2$ if $G=D_{20}$ ? Some power of $2+a^2$ etc? I only know how to define group Algebra in GAP
gap>h:=FreeGroup("a","b");
gap>g:=h/[h.1^n, h.2^2, h.2*h.1*h.2^-1.h.1]
gap>FG:=GroupRing(GF(p), G);
I am tried as $x:=( 2+h.1*h.1)^2$ but unable to calculate . Please help .