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ABCD ABCD Geometric group theory

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

$$ \int_a^b f(x) \ dx $$

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

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

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.