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Is there a connection between a special group (i.e. a p-group with its derived group, center and frattini subgroup all equal) and the special linear group (i.e. group of matrices with determinant=1)? I've seen the first one in finite group theory and the other one in linear algebra so I'm not sure if there's something more to it or not.

Thanks in advance

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  • $\begingroup$ Probably not. I suspect that "special" has several unrelated meanings in different contexts as is the case with many adjectives in mathematics (like "normal" and "regular"). $\endgroup$ – Ben Grossmann Dec 5 '20 at 16:41
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Not really -- there are too few words available to assign a common term for all situations one would like to distinguish. So the defined term is not "special" but "special linear", respectively "special $p$-group".

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