The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the theory. Group theory is a powerful formal method for analyzing abstract and physical systems in which symmetry is present and has surprising importance in physics, especially quantum mechanics.
Group Theory
See also
Finite Group, Group, Higher Dimensional Group Theory, Plethysm, Symmetry Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
References
Alperin, J. L. and Bell, R. B. Groups and Representations. New York: Springer-Verlag, 1995.Arfken, G. "Introduction to Group Theory." §4.8 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 237-276, 1985.Burnside, W. Theory of Groups of Finite Order, 2nd ed. New York: Dover, 1955.Burrow, M. Representation Theory of Finite Groups. New York: Dover, 1993.Carmichael, R. D. Introduction to the Theory of Groups of Finite Order. New York: Dover, 1956.Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, 1985.Cotton, F. A. Chemical Applications of Group Theory, 3rd ed. New York: Wiley, 1990.Dixon, J. D. Problems in Group Theory. New York: Dover, 1973.Farmer, D. Groups and Symmetry. Providence, RI: Amer. Math. Soc., 1995.Grossman, I. and Magnus, W. Groups and Their Graphs. Washington, DC: Math. Assoc. Amer., 1965.Hamermesh, M. Group Theory and Its Application to Physical Problems. New York: Dover, 1989.Lomont, J. S. Applications of Finite Groups. New York: Dover, 1987.Magnus, W.; Karrass, A.; and Solitar, D. Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations. New York: Dover, 1976.McLain, W. M. Symmetry Theory in Molecular Physics with Mathematica. New York: Springer, 2008.Mirman, R. Group Theory: An Intuitive Approach. River Edge, NJ: World Scientific, 1995.Robinson, D. J. S. A Course in the Theory of Groups, 2nd ed. New York: Springer-Verlag, 1995.Rose, J. S. A Course on Group Theory. New York: Dover, 1994.Rotman, J. J. An Introduction to the Theory of Groups, 4th ed. New York: Springer-Verlag, 1995.Scott, W. R. Group Theory. New York: Dover, 1987.Weisstein, E. W. "Books about Group Theory." http://www.ericweisstein.com/encyclopedias/books/GroupTheory.html.Weyl, H. The Classical Groups: Their Invariants and Representations. Princeton, NJ: Princeton University Press, 1997.Wybourne, B. G. Classical Groups for Physicists. New York: Wiley, 1974.Referenced on Wolfram|Alpha
Group TheoryCite this as:
Weisstein, Eric W. "Group Theory." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GroupTheory.html