Classification of finite simple groups: Difference between revisions

Revision as of 13:56, 7 October 2024

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Simple groups can be seen as the basic building blocks of all [[finite group]]s, reminiscent of the way the [[prime number]]s are the basic building blocks of the [[natural number]]s (the natural number/s 0 and/or 1 cannot be built from the primes). The [[Jordan–Hölder theorem]] is a more precise way of stating this fact about finite groups. However, a significant difference from [[integer factorization]] is that such "building blocks" do not necessarily determine a unique group, since there might be many non-[[isomorphic]] groups with the same [[composition series]] or, put in another way, the [[group extension#Extension problem|extension problem]] does not have a unique solution.

[[Daniel Gorenstein|Gorenstein]] (d.1992), [[Richard Lyons (mathematician)|Richard Lyons]], and [[Ronald Solomon|Solomon]] are gradually publishing a simplified and revised version of the proof.

==Statement of the classification theorem==