Or, at least, of an arithmetic subgroup of a semisimple Lie group:

- The “subgroup of integer points” is an arithmetic group …
- …
*if embedded in a reasonable way which doesn’t distort the arithmetic structure—*slightly more precisely, if it is [essentially] an algebraic group over the rationals.
- Anything isomorphic to a finite extension is arithmetic too.

For a more precise definition—Witte Morris’ book is a good place to start; he fudges over a few things too, but actually has references to fill those in …

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