Uses of the holomorph, Hol($G$) = $G \\rtimes $ Aut($G$)
https://mathoverflow.net/questions/13897/uses-of-the-holomorph-holg-g-rtimes-autg
WebThe holomorph is called the affine general linear group, AGL(n,p), which can be thought of as (n+1)×(n+1) matrices [ A, v ; 0, 1 ] where A in Aut(G) ≅ GL(n,p) and v in G ≅ (Z/pZ)^n. If you restrict the automorphism group to only include GF(p^k) automorphisms, where k divides n, then you get a subgroup AGL(n/k,p^k) that is also important.
DA: 10 PA: 83 MOZ Rank: 83