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1. • CommentRowNumber1.
   • CommentAuthorTobyBartels
   • CommentTimeJul 1st 2010
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexWhat's canonical about a [[canonical hypergroup]]? Is there any other [[hypergroup]]?

   What’s canonical about a canonical hypergroup? Is there any other hypergroup?

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 1st 2010
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   Author: David_Corfield
   Format: MarkdownItexMaybe [this paper](http://journals.cambridge.org/action/displayFulltext?type=1&fid=4764672&jid=BAZ&volumeId=20&issueId=01&aid=4764664) has the answer. It looks like hypergroups arose (partly) in the study of conjugacy classes and characters of groups, when you have a situation where you wonder how many copies of a third thing are contained in some product of a first and second thing. The underlying canonical hypergroup then records those components appearing in the composition of two things. I imagine the whole field is a mess in terms of organisation. Apparently sometimes hypergroups are called multigroups or polygroups.

   Maybe this paper has the answer. It looks like hypergroups arose (partly) in the study of conjugacy classes and characters of groups, when you have a situation where you wonder how many copies of a third thing are contained in some product of a first and second thing. The underlying canonical hypergroup then records those components appearing in the composition of two things.

   I imagine the whole field is a mess in terms of organisation. Apparently sometimes hypergroups are called multigroups or polygroups.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 2nd 2010
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   Author: David_Corfield
   Format: MarkdownItexI've posed some of our questions at [MO](http://mathoverflow.net/questions/30288/what-are-hypergroups-and-hyperrings-good-for).

   I’ve posed some of our questions at MO.