User:Ian Clark/IAC72/crib

Stock formulae for copy/paste into User:Ian_Clark/IAC72

Symbol list: [1]

AA

$\displaystyle G=ASB$

$\displaystyle A$ and $\displaystyle B$

$\displaystyle S$

$\displaystyle g\in G$

$\displaystyle asb$ or $\displaystyle b's'a'$

$\displaystyle a\in A$ ;   $\displaystyle b\in B$

$\displaystyle a\in A$ ;   $\displaystyle s\in S$ ;   $\displaystyle b\in B$

$\displaystyle a,a'\in A$ ;   $\displaystyle s,s'\in S$ ;   $\displaystyle b,b'\in B$

AB

$\displaystyle \{A,S,B,\chi\}$

$\displaystyle \chi$

$\displaystyle ASB$

the $\displaystyle A$ -commuting condition

Zappa product: $\displaystyle AB | A \cap B=E$

$\displaystyle A=D_4$

$\displaystyle ab$ or $\displaystyle b'a'$

$\displaystyle a,a' \in A; b,b' \in B$

the set $\displaystyle \{ab | a,a' \in A; b,b' \in B\}$

$\displaystyle G=AB=BA | A \cap B=E$

$\displaystyle b'=g^{-1}a'g$   for some $\displaystyle g\in G$
$\displaystyle g=ab$   for some $\displaystyle a\in A$ ; $\displaystyle b\in B$

$\displaystyle 0=X_0\subset X_1\subset \dots \subset X_n=A$
$\displaystyle A=X_0\supset X_1\supset \dots \supset X_n=0$
$\displaystyle A=X_0\supseteq X_1\supseteq \dots \supseteq X_n=0$
$\displaystyle A=X_0\supsetneq X_1\supsetneq \dots \supsetneq X_n=0$
$\displaystyle 1 = G_0\triangleleft G_1\triangleleft \cdots \triangleleft G_n = G,$
$\displaystyle G = G_0\triangleright G_1\triangleright \cdots \triangleright G_n = 1,$

AC

$\displaystyle a\in A; b\in B$

$\displaystyle a\in A; b\in B$

$\displaystyle a\in A; b\in B$

$\displaystyle a\in A ; b\in B$

$\displaystyle {a\in A} ; {b\in B}$

$\displaystyle a\in A$ ; $\displaystyle b\in B$

$\displaystyle a\in A$ ;   $\displaystyle b\in B$

$\displaystyle A \circ B$

AE

A * B $\displaystyle A * B$

A / B $\displaystyle A / B$

A * B $\displaystyle A * B$

A / B ${\displaystyle A/B}$

A \# B ${\displaystyle A\#B}$

A \% B ${\displaystyle A\%B}$

A \& B ${\displaystyle A\&B}$