Many years ago I found in google the notation "Holomorph of group". It is the semi direct product of $G$ with $Aut(G)$. Why is the term "Holomorph" used here, while it is usually used for complex analytic functions? More information on this object is very appreciated.

  • 4
    $\begingroup$ I don't know anything about holomorph groups, but it's probably a word of Greek origin, meaning something like "complete form", "completely formed" or so.. $\endgroup$ – Qfwfq Jan 17 '15 at 8:48
  • 5
    $\begingroup$ One nice way to consider the holomorph is as the normalizer of the left regular representation in the group of permutations of elements. $\endgroup$ – S. Carnahan Jan 17 '15 at 10:18
  • 1
    $\begingroup$ according to Wikipedia, the name holomorph was introduced by Briot and Bouquet --- en.citizendium.org/wiki/Holomorphic_function $\endgroup$ – Carlo Beenakker Jan 17 '15 at 16:03

I'm not a history expert, but according to Miller, Blichfeldt and Dickson: "Theory and applications of finite groups" (1916), footnote p. 46: "The concept of holomorph was used by many early writers, but the term was introduced by W. Burnside in the first edition of his Theory of Groups, 1897, p. 228."

  • 2
    $\begingroup$ Yes, what was introduced by the people Carlos Beenakker mentions was the term "holomorphic function" ( at least according to Wikipedia). $\endgroup$ – Geoff Robinson Jan 17 '15 at 18:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.