Abstract Group

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 C_2×C_2 and the cyclic group C4. A number of particular examples of the abstract group C_4 are the point groups C_4 (unfortunately, the symbols for the point groups C_n are the same as those for the abstract cyclic groups C_n to which they are isomorphic) and Z_4.

See also

Finite Group, Group

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

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Abstract Group

Cite this as:

Weisstein, Eric W. "Abstract Group." From MathWorld--A Wolfram Web Resource.

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