Ronnie Brown wrote:
I would like to raise an objection to using the term `2-group' as on nlab and elsehere since for the group theorists this has a specialised meaning: See the following wiki entry, especially the first 2 words:
"In mathematics, given a prime number p, a p-group is [...]"
That the first 2 words are "In mathematics" rather than "In group theory, a branch of mathematics," means nothing. It's not like the Wikipedians had a discussion about it and determined that p-groups appear throughout mathematics. You do raise a good point, though. The term '2-group' is a special case of both 'p-group' and 'n-group', and these mean very different things. I wouldn't want to give up 'n-group', so I find '2-group' appropriate when (as on the n-Category Lab) one is discussing n-groups as well. But in your example about the structure of finite crossed modules, one can simply say 'crossed module', making a note that some literature calls a crossed module a '2-group' (or even 'strict 2-group').
"[...] Such groups are also called primary." there are claims that crossed modules, for example, can be thought of as `2-dimensional groups'
In extreme cases, these show the way: both 'p-group' and 'n-group' are abbreviations, for 'p-primary group' and 'n-dimensional higher group'. So one can always use the full name or specify which usage one's paper follows. --Toby