End MatrixGroups.
Delimit Scope abelem_scope with Mg.
Open Scope abelem_scope.
Definition abelem_dim' (gT : finGroupType) (E : {set gT}) :=
(logn (pdiv #|E|) #|E|).-1.
Arguments abelem_dim' {gT} E%g.
Notation "''dim' E" := (abelem_dim' E).+1
(at level 10, E at level 8, format "''dim'  E") : abelem_scope.
Notation "''rV' ( E )" := 'rV_('dim E)
(at level 8, format "''rV' ( E )") : abelem_scope.
Notation "''M' ( E )" := 'M_('dim E)
(at level 8, format "''M' ( E )") : abelem_scope.
Notation "''rV[' F ] ( E )" := 'rV[F]_('dim E)
(at level 8, only parsing) : abelem_scope.
Notation "''M[' F ] ( E )" := 'M[F]_('dim E)
(at level 8, only parsing) : abelem_scope.
Section AbelemRepr.
Section FpMatrix.
Variables p m n : nat.
Local Notation Mmn := 'M['F_p]_(m, n).

Lemma mx_Fp_abelem : prime p -> p.-abelem [set: Mmn].
End FpMatrix.