diff options
| author | Cyril Cohen | 2018-02-06 19:36:53 +0100 |
|---|---|---|
| committer | GitHub | 2018-02-06 19:36:53 +0100 |
| commit | d6bc72cd477ed6fe8b95782b26a2e0fc92711395 (patch) | |
| tree | 6996e39182b97573b1cdecaeb7c8c8a3f58c1e77 /mathcomp/odd_order/BGsection6.v | |
| parent | 11e539dae1bfe8bc67fc7bd1eb65ee3b4c29f813 (diff) | |
| parent | f3ce9ace4b55654d6240db9eb41a6de3c488f0d9 (diff) | |
Merge pull request #164 from CohenCyril/linting
linting of the whole library
Diffstat (limited to 'mathcomp/odd_order/BGsection6.v')
| -rw-r--r-- | mathcomp/odd_order/BGsection6.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/mathcomp/odd_order/BGsection6.v b/mathcomp/odd_order/BGsection6.v index e344b98..9e06b1a 100644 --- a/mathcomp/odd_order/BGsection6.v +++ b/mathcomp/odd_order/BGsection6.v @@ -31,7 +31,7 @@ Implicit Type p : nat. Section OneType. -Variable gT : finGroupType. +Variable gT : finGroupType. Implicit Types G H K S U : {group gT}. (* This is B & G, Theorem A.4(b) and 6.1, or Gorenstein 6.5.2, the main Hall- *) @@ -77,7 +77,7 @@ case/sdprodP=> _ defG nKH tiKH coKH solK sKG'. set K' := K^`(1); have [sK'K nK'K] := andP (der_normal 1 K : K' <| K). have nK'H: H \subset 'N(K') := gFnorm_trans _ nKH. set R := [~: K, H]; have sRK: R \subset K by rewrite commg_subl. -have [nRK nRH] := joing_subP (commg_norm K H : K <*> H \subset 'N(R)). +have [nRK nRH] := joing_subP (commg_norm K H : K <*> H \subset 'N(R)). have sKbK'H': K / R \subset (K / R)^`(1) * (H / R)^`(1). have defGb: (K / R) \* (H / R) = G / R. by rewrite -defG quotientMl ?cprodE // centsC quotient_cents2r. @@ -90,7 +90,7 @@ have{sKbK'H' tiKbHb'} derKb: (K / R)^`(1) = K / R. have{derKb} Kb1: K / R = 1. rewrite (contraNeq (sol_der1_proper _ (subxx (K / R)))) ?quotient_sol //. by rewrite derKb properxx. -have{Kb1 sRK} defKH: [~: K, H] = K. +have{Kb1 sRK} defKH: [~: K, H] = K. by apply/eqP; rewrite eqEsubset sRK -quotient_sub1 ?Kb1 //=. split=> //; rewrite -quotient_sub1 ?subIset ?nK'K //= -/K'. have cKaKa: abelian (K / K') := der_abelian 0 K. @@ -255,7 +255,7 @@ Qed. (* This is B & G, Lemma 6.6(d). *) Lemma plength1_Sylow_Jsub (Q : {group gT}) : Q \subset G -> p.-group Q -> - exists2 x, x \in 'C_G(Q :&: S) & Q :^ x \subset S. + exists2 x, x \in 'C_G(Q :&: S) & Q :^ x \subset S. Proof. move=> sQG pQ; have sQ_Gp'p: Q \subset 'O_{p^',p}(G). rewrite -sub_quotient_pre /= pcore_mod1 ?(subset_trans sQG) //. @@ -278,7 +278,7 @@ End OneType. Theorem plength1_norm_pmaxElem gT p (G E L : {group gT}) : E \in 'E*_p(G) -> odd p -> solvable G -> p.-length_1 G -> L \subset G -> E \subset 'N(L) -> p^'.-group L -> - L \subset 'O_p^'(G). + L \subset 'O_p^'(G). Proof. move=> maxE p_odd solG pl1G sLG nEL p'L. case p_pr: (prime p); last first. |
