. ▁His ▁aut obi ography , ▁I ▁Pol iced ▁Toronto , ▁was ▁published ▁in ▁ 1 9 8 5 . ▁ ▁Mack ey ▁retired ▁to ▁Bra ce bridge , ▁Ontario ▁where ▁he ▁died ▁at ▁the ▁age ▁of ▁ 9 5 . ▁ ▁References ▁ ▁Category : T or onto ▁police ▁chief s ▁Category : 1 9 1 3 ▁birth s ▁Category : 2 0 0 9 ▁death s <0x0A> </s> ▁In ▁mathematics , ▁in ▁the ▁field ▁of ▁group ▁theory , ▁a ▁subgroup ▁H ▁of ▁a ▁given ▁group ▁G ▁is ▁a ▁sub normal ▁subgroup ▁of ▁G ▁if ▁there ▁is ▁a ▁finite ▁chain ▁of ▁sub groups ▁of ▁the ▁group , ▁each ▁one ▁normal ▁in ▁the ▁next , ▁beginning ▁at ▁H ▁and ▁ending ▁at ▁G . ▁ ▁In ▁notation , ▁ ▁is ▁- sub normal ▁in ▁ ▁if ▁there ▁are ▁sub groups ▁ ▁of ▁ ▁such ▁that ▁ ▁is ▁normal ▁in ▁ ▁for ▁each ▁. ▁ ▁A ▁sub normal ▁subgroup ▁is ▁a ▁subgroup ▁that ▁is ▁- sub normal ▁for ▁some ▁positive ▁integer ▁. ▁Some ▁facts ▁about ▁sub normal ▁sub groups : ▁ ▁A ▁ 1 - sub normal ▁subgroup ▁is ▁a ▁proper ▁normal ▁subgroup ▁( and ▁vice ▁vers a ). ▁ ▁A ▁finit ely ▁generated ▁group ▁is ▁nil pot ent ▁if ▁and ▁only ▁if ▁each ▁of ▁its ▁sub groups ▁is ▁sub normal . ▁ ▁Every ▁qu as in ormal ▁subgroup , ▁and , ▁more ▁generally , ▁every ▁conjug ate - per mutable ▁subgroup , ▁of ▁a ▁finite ▁group ▁is ▁sub normal . ▁ ▁Every ▁pron ormal