Complete holomorphs

Multiple Holomorphs of Dihedral and Quaternionic Groups

The holomorph of a group G is NormB(λ(G)), the normalizer of the left regular representation λ(G) in its group of permutations B = Perm(G). The multiple holomorph of G is the normalizer of the holomorph in B. The multiple holomorph and its quotient by the holomorph encodes a great deal of information about the holomorph itself and about the group λ(G) and its conjugates within the holomorph. We...

Homology of Holomorphs of Free Groups

The holomorph of a free group Fn is the semidirect product FnoAut(Fn). Using the methods of Hatcher and Vogtmann in [10] and [11], we derive stability results and calculate the mod-p homology of these holomorphs for odd primes p in dimensions 1 and 2, and their rational homology in dimensions 1 through 5. Calculations of the twisted (where Aut(Fn) acts by first projecting to Gln(Z) and then inc...

Some Observations regarding the Holomorphs of Finite Abelian Groups

Presentations for the holomorphs of abelian groups of the form Cpn × 1 for p=2 or an odd prime are given. These presentations extend the results given in Burnside’s well-known text on finite groups on the holomorphs for the cyclic groups of orders p for p being an odd or even prime. The following set of observations all deal with the holomorphs of finite abelian groups. The motivation here is t...

Complete Issue 2016-2

Complete knee replacement surgery

In normal activities such as walking, rn­ning, kneeling, climbing stairs and gettmg in and out of chairs the loa pu OI.the human knee joint can exceed five times the weight of the body. Nowadays large num­bers of people make ! urtrer d mands on the knee in participatmg 1_n sucli sport  as football, tennis and long distance runnng. It is no wonder that many people go mto their later years with o...