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proux01 committed Nov 29, 2023
1 parent 6fa8ce4 commit 3a97b71
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Showing 5 changed files with 7 additions and 7 deletions.
2 changes: 1 addition & 1 deletion theories/BGsection12.v
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Expand Up @@ -306,7 +306,7 @@ have SylowE3 P: Sylow E3 P -> [/\ cyclic P, P \subset E^`(1) & 'C_P(E) = 1].
have sP_Ep'P: P \subset 'O_p^'(E) <*> P := joing_subr _ _.
have sylP_Ep'P := pHall_subl sP_Ep'P (normal_sub nsEp'P_E) sylP_E.
rewrite -{2}(Frattini_arg nsEp'P_E sylP_Ep'P) /= !norm_joinEr //.
by rewrite -mulgA (normC nPK) -mulPK -{1}(mulGid P) !mulgA.
by rewrite -[LHS]mulgA (normC nPK) -mulPK -{1}(mulGid P) !mulgA.
have ntPE': P :&: E^`(1) != 1.
have sylPE' := Hall_setI_normal (der_normal 1 E) sylP_E.
rewrite -rank_gt0 (rank_Sylow sylPE') p_rank_gt0.
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2 changes: 1 addition & 1 deletion theories/BGsection2.v
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Expand Up @@ -1138,7 +1138,7 @@ split.
have Ur: r \in GRing.unit.
by rewrite -(unitrX_pos _ (prime_gt0 q_pr)) rq1 unitr1.
pose u_r : {unit 'F_p} := Sub r Ur; have:= order_dvdG (in_setT u_r).
rewrite card_units_Zp ?pdiv_gt0 // {2}/pdiv primes_prime //=.
rewrite card_units_Zp ?pdiv_gt0 // [X in totient X]/pdiv primes_prime //=.
rewrite (@totient_pfactor p 1) // muln1; apply: dvdn_trans.
have: (u_r ^+ q == 1)%g.
by rewrite -val_eqE unit_Zp_expg -Zp_nat natrX natr_Zp rq1.
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2 changes: 1 addition & 1 deletion theories/BGsection3.v
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Expand Up @@ -548,7 +548,7 @@ have irrK'K: mx_absolutely_irreducible rK'K.
by rewrite mem_enum.
by rewrite PackSocleK.
have [i def_i]: exists i, [set: sK'G'] = [set i].
apply/cards1P; rewrite -dvdn1 -{7}(eqnP coKp) dvdn_gcd.
apply/cards1P; rewrite -dvdn1 -[X in _ %| X](eqnP coKp) dvdn_gcd.
by rewrite -{1}eq_sK' sK'_dv_K sK'_dv_p.
pose M := socle_base i; have simM : mxsimple rK'G' M := socle_simple i.
have cycGq: cyclic (G' / K^`(1)).
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2 changes: 1 addition & 1 deletion theories/PFsection13.v
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Expand Up @@ -706,7 +706,7 @@ suffices{ub_alpha} lb_a1_2: a1_2 >= #|H^#|%:R.
rewrite ler_pMl ?(lt_le_trans _ lb_a1_2) ?ler1n ?ltr0n //.
by rewrite -(subnKC Pgt2).
have:= leq_trans (ltnW Pgt2) (subset_leq_card sPH).
by rewrite (cardsD1 1%g) group1.
by rewrite [in X in X -> _](cardsD1 1%g) group1.
have /CnatP[n Dn]: '[alpha] \in Cnat by rewrite Cnat_cfnorm_vchar.
have /CnatP[m Dm]: a1_2 \in Cnat by rewrite Cnat_exp_even ?Cint_vchar1.
rewrite Dm leC_nat leqNgt; apply: contra suma_lt_H => a1_2_lt_H.
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6 changes: 3 additions & 3 deletions theories/PFsection9.v
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Expand Up @@ -531,8 +531,8 @@ have cEE A: A \in E_U -> centgmx rU A.
apply/row_matrixP=> i; rewrite row_mul; move: (row i _) => h.
have cHbH': (U / H0)^`(1) \subset 'C(Hbar).
by rewrite -quotient_der ?quotient_cents.
apply: rVabelem_inj; rewrite rVabelemJ ?groupR //.
by apply: (canLR (mulKg _)); rewrite -(centsP cHbH') ?mem_commg ?mem_rVabelem.
apply: rVabelem_inj; rewrite rVabelemJ ?groupR //; apply: (canLR (mulKg _)).
by rewrite -[LHS](centsP cHbH')// ?mem_commg ?mem_rVabelem.
have{cEE} [F [outF [inF outFK inFK] E_F]]:
{F : finFieldType & {outF : {rmorphism F -> 'M(Hbar)%Mg}
& {inF : {additive _ -> _} | cancel outF inF & {in E_U, cancel inF outF}}
Expand Down Expand Up @@ -1013,7 +1013,7 @@ have sW1_Imu i: W1 \subset 'I[theta (mu_f i) %% H0]%CF.
have W1w1w: (w1 * (inMb w)^-1)%g \in W1bar by rewrite !in_group.
rewrite -(cfResE _ (sH1wH _ W1w1w)) -?mem_conjg -?conjsgM ?mulgKV ?H1x //.
rewrite -(cfResE _ (sH1wH _ W1w1)) ?H1x ?cfBigdprodKabelian //.
rewrite !ffunE W1w1 W1w1w -[x w1](conjgKV w1) -conjgM !isom_IirrE.
rewrite !ffunE W1w1 W1w1w -[x w1](conjgKV w1) -(conjgM _ w1) !isom_IirrE.
by rewrite !cfIsomE -?mem_conjg ?H1x.
have inj_mu: {in predC1 0 &, injective (fun i => cfIirr (mk_mu i))}.
move=> i1 i2 nz_i1 nz_i2 /(congr1 (tnth (irr HU))).
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