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Finite Group Z2


The unique group of Order 2. $Z_2$ is both Abelian and Cyclic. Examples include the Point Groups $C_s$, $C_i$, and $C_2$, the integers modulo 2 under addition, and the Modulo Multiplication Groups $M_3$, $M_4$, and $M_6$. The elements $A_i$ satisfy ${A_i}^2=1$, where 1 is the Identity Element. The Cycle Graph is shown above, and the Multiplication Table is given below.

$Z_2$ 1 $A$
1 1 $A$
$A$ $A$ 1

The Conjugacy Classes are $\{1\}$ and $\{A\}$. The irreducible representation for the $C_2$ group is $\{1,-1\}$.

© 1996-9 Eric W. Weisstein