An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct abstract groups on four elements: the vierergruppe and the cyclic group C4. A number of particular examples of the abstract group are the point groups (unfortunately, the symbols for the point groups are the same as those for the abstract cyclic groups to which they are isomorphic) and .

# Abstract Group

## See also

Finite Group, Group## Explore with Wolfram|Alpha

## References

Shanks, D.*Solved and Unsolved Problems in Number Theory, 4th ed.*New York: Chelsea, pp. 74 and 85, 1993.

## Referenced on Wolfram|Alpha

Abstract Group## Cite this as:

Weisstein, Eric W. "Abstract Group." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AbstractGroup.html