Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups and are isomorphic groups, written or (Shanks 1993).

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

CITE THIS AS:

Weisstein, Eric W. "Isomorphic Groups." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IsomorphicGroups.html