Isomorphic Groups

Two Groups are isomorphic if the correspondence between them is One-to-One and the ``multiplication'' table is preserved. For example, the Point Groups $C_2$ and $D_1$ are isomorphic Groups, written $C_2\cong D_1$ or $C_2\rightleftharpoons D_1$ (Shanks 1993). Note that the symbol $\cong$ is also used to denote geometric Congruence.

References

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.