feat: add Baer-Suzuki theorem eval problem#311
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This PR adds the Baer-Suzuki theorem: an element x of a finite group G lies in the p-core O_p(G) iff every pair (x, x^g) of conjugates generates a p-group. Baer (1957) for p = 2, Suzuki (1965) in general; a standard tool in CFSG-era local analysis. Introduces LeanEval/GroupTheory/Defs/PCore.lean defining O_p(G) as the supremum of normal p-subgroups, since Mathlib has no `pCore` operation. 🤖 Prepared with Claude Code
The original docstring incorrectly stated that the supremum of normal p-subgroups is only a p-group for finite G. In fact the family of normal p-subgroups is directed under ≤ (the join of two normal p-subgroups is again a normal p-subgroup, by Subgroup.sup_normal and IsPGroup.to_sup_of_normal_left), so by Subgroup.mem_iSup_of_directed every element of the supremum already lies in one of the summands, hence has p-power order. So pCore p G is always a p-group, regardless of |G|. 🤖 Prepared with Claude Code
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This PR adds the Baer-Suzuki theorem: an element
xof a finite groupGlies in thep-coreO_p(G)iff every pair(x, x^g)of conjugates generates ap-group. Baer (1957) forp = 2, Suzuki (1965) in general; a standard tool in CFSG-era local analysis, used together with the Bender method and signalizer functor theory.Introduces
LeanEval/GroupTheory/Defs/PCore.leandefiningO_p(G)as the supremum of normalp-subgroups, since Mathlib has nopCoreoperation.🤖 Prepared with Claude Code