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ABCD ABCD Geometric group theory

${\begin{array}{ccc}A&{\stackrel {a}{\rightarrow }}&B\\\downarrow \scriptstyle {b}&&\downarrow \scriptstyle {c}\\C&{\stackrel {d}{\rightarrow }}&D\end{array}}$

$\int _{a}^{b}f(x)\ dx$

${\begin{array}{ccccc}A&\rightarrow &B&\leftarrow &C\\&\searrow &\downarrow &\swarrow \\&&D\end{array}}$

${\begin{array}{ccccc}A&{\xrightarrow {\text{label}}}&B&{\xleftarrow {\text{label}}}&C\\&\searrow &{\Big \downarrow }{\scriptstyle \alpha }&\swarrow \\&&D\end{array}}$

In the mathematical subject of group theory, a just infinite group is a group which is infinite but all of whose proper quotients are finite. Just infinite groups play a prominent role in the theory of higher rank lattices and in the theory of ``self-similar" groups such as the Grigorchuk group of intermediate growth.