single word requests - What is gender neutral for fraternity/sorority?

Is there a gender neutral form for "fraternity/sorority"? How about "brotherhood/sisterhood"?

Example: As in "If mathematicians were to form a fraternity of scholars, as in yet another alpha beta omega club, their hazing rite would be ...". Wikipedia article suggests such organizations are meant to be gender exclusive. So perhaps no words exist to suggest a club of both sexes which otherwise has chracteristics of Greek organizations.

Answer

Most co-ed fraternities are called "fraternities" (though I do know of one co-ed sorority; it was originally women-only, and retained the label "sorority" when it opened its doors to men).

However, there are some serious problems with your example:

• The phrase "fraternity of scholars" is already well-attested, and almost never refers to a Greek organization; rather, it's generally either figurative, or referring to co-ed groups like Phi Beta Kappa.
  
  
  
  
  • Note that Phi Beta Kappa, despite being a fraternity, and despite being named with Greek letters, is not a "Greek organization", and will not evoke the Animal House image that you seem to have in mind.
  
  


• Even without that phrase, when you talk about mathematicians forming a fraternity, people are likely to think of a professional fraternity. There are actually quite a few math fraternities, and most of them are co-ed, but (like Phi Beta Kappa) they are not "Greek organizations" and will not evoke a Animal House image. Even readers who are not familiar with any math fraternities, specifically, are likely to picture something along these lines: there exist chemistry fraternities, engineering fraternities, and so on, so a math fraternity is a natural idea.



• More generally — no co-ed fraternities are "Greek organizations". There's no gender-neutral way to evoke the Animal House image.


• A large proportion of Americans have belonged to fraternities and sororities that are Greek organizations — and the majority of these do not haze. You should consider whether you really want to turn off a good chunk of your readership by presupposing that they conform to a negative stereotype. (It's a bit like writing, "When women mathematicians get together, their catfights are […]" . . . no matter where you might go with it, you've lost a chunk of your audience. Though to be sure, a hazing joke will not be anywhere near as offensive as a catfight joke.)

If your goal is just to set up a joke about mathematics-themed hazing, I'd suggest writing something like, "When mathematicians haze each other, it's by […]". Your readers will get that it's a joke. It doesn't require lots of setup.

(By the way — "brotherhood" can also be gender-neutral, but it never conveys the specific idea of a Greek organization.)