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Results tagged with linear-groups
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user 4231
7
votes
Minimal number of generators for $GL(n,\mathbb{Z})$
Though it's a good exercise to work things out directly (as YCor does), the ideas here are all fairly old and can be extracted without much difficulty from the literature as Dietrich's reference indic …
- 52.9k
23
votes
Isomorphic general linear groups implies isomorphic fields?
The answer to the question is yes, though I don't have all the old literature at my fingertips. This kind of question for various classes of linear groups has a long history in the study of homomorphi …
- 52.9k
3
votes
Sylow subgroups of projective general linear groups
To reinforce Geoff Robinson's cautious comment, I'd encourage you to dig into a volume of the ongoing treatise by Gorenstein-Lyons-Solomon The Classification of the Finite Simple Groups, Number 3 (Am …
- 52.9k