Revision as of 03:54, 12 December 2023 edit PonTRexMaximus (talk \| contribs) 27 edits m Improved grammar by removing "it" in a list which describes qualities Tag: Visual edit ← Previous edit		Revision as of 19:51, 20 December 2023 edit undo Scrooge Mcduc (talk \| contribs) Extended confirmed users 651 edits →Statement of the classification theorem: "derived subgroup" is probably less confusing to most readers, as "derivative" may give the wrong impression. I may also just be wrong here, so feel free to change this back if you disagree. Tags: Mobile edit Mobile web edit Next edit →
Line 15: the [[alternating groups]] of degree at least 5, the [[groups of Lie type]], ** the [[commutator subgroup\|~~derivative~~derived subgroup]] of the groups of Lie Type, such as the [[Tits group]]<ref group="note" name="tits">The infinite family of [[Ree group#Ree groups of type 2F4\|Ree groups of type {{math\|<sup>2</sup>F<sub>4</sub>(2<sup>2''n''+1</sup>)}}]] contains only finite groups of Lie type. They are simple for {{math\|''n''≥1}}; for {{math\|''n''{{=}}0}}, the group {{math\|<sup>2</sup>F<sub>4</sub>(2)}} is not simple, but it contains the simple [[commutator subgroup]] {{math\|<sup>2</sup>F<sub>4</sub>(2)′}}. So, if the infinite family of commutator groups of type {{math\|<sup>2</sup>F<sub>4</sub>(2<sup>2''n''+1</sup>)′}} is considered a systematic infinite family (all of Lie type except for {{math\|''n''{{=}}0}}), the Tits group {{math\|T :{{=}} <sup>2</sup>F<sub>4</sub>(2)′}} (as a member of this infinite family) is not sporadic.</ref> * one of 26 groups called the "[[sporadic groups]]" }}

Classification of finite simple groups: Difference between revisions