some changes

study/Imperial_mathematics/year_2/Groups_and_Rings/Part_1_Groups/1_The_Algebriac_Structure_of_Groups.md

@@ -10,12 +10,13 @@ $$\gdef\N{\mathbb{N}}$$
 $$\gdef\Q{\mathbb{Q}}$$
 $$\gdef\F{\mathcal{F}}$$
 $$\gdef\iso{\overset{\sim}{=}}$$
-$$\gdef\ke{\operatorname{Ker}}$$
-$$\gdef\im{\operatorname{Im}}$$
-$$\gdef\lcm{\operatorname{lcm}}$$
-$$\gdef\gcd{\operatorname{gcd}}$$
-$$\gdef\ord#1{\operatorname{ord(#1)}}$$
-$$\gdef\sgn{\operatorname{sgn}}$$
+$$\gdef\ke{\textsf{Ker}}$$
+$$\gdef\im{\textsf{Im}}$$
+$$\gdef\lcm{\textsf{lcm}}$$
+$$\gdef\gcd{\textsf{gcd}}$$
+$$\gdef\mod{\textsf{mod}}$$
+$$\gdef\ord#1{\textsf{ord(#1)}}$$
+$$\gdef\sgn{\textsf{sgn}}$$
 $$\gdef\bluetext#1{\blue{\textsf{#1}}}$$
 $$\gdef\bluemath#1{\blue{\mathsf{#1}}}$$
 $$\gdef\def{\blue{\textsf{def}}}$$