I was reading a Hypergraph Isomorphism than I encounter a new term called " supergroup ", I know what a subgroup means but about supergroup I don't know anything. I tried to read from the wikipedia and get this :

The concept of supergroup is a generalization of that of group. In other words, every supergroup carries a natural group structure, but there may be more than one way to structure a given group as a supergroup.

Even after reading his I am feeling like I am not getting the feeling that I have understood the definition of supergroup.

Please explain the defintion of supergroup with example and what is its significance in group theory.

Thanks in advance.

Reference : https://en.wikipedia.org/wiki/Supergroup_(physics) (Please note that in this article they have defined the term " Lie supergroup " but I am asking about " supergroup ". I don't know these two terms are same or different)

  • $\begingroup$ Why don't you quote the definition of a supergroup? The passage you quoted is not a definition. Better yet, why don't you tell us what book or web page you quoted that passage from? You hinted that it's from a Wikipedia article. Which Wikipedia article is that? $\endgroup$ – bof Aug 6 '17 at 7:16
  • $\begingroup$ @ bof I have linked the wikipedia page. $\endgroup$ – user275490 Aug 6 '17 at 7:44
  • $\begingroup$ As you note, the Wiki page defines only Lie supergroup ... a group object in the category of supermanifolds. It does not state the definition, or even say there is such a thing, as supergroup alone. $\endgroup$ – GEdgar Aug 6 '17 at 12:11
  • 1
    $\begingroup$ As https://en.wikipedia.org/wiki/Supergroup says, it is "a rarely used term in mathematics for the counterpart of a subgroup." That is, if $H$ is a subgroup of $G$, then $G$ is a supergroup of $H$. This has nothing to do with the notion from super Lie theory. $\endgroup$ – anon Aug 15 '17 at 4:37

Your Answer

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