Abstract
In addition to the topics in the title, this chapter presents the operations of direct product and sum, quotient group, the Noether homomorphism theorems, the Zassenhaus butterfly lemma, and exercises on permutation and alternating groups, solvable and nilpotent groups, simple groups, the Sylow theorems, and the basic theorems for abelian groups.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
General References
Artin, E.: Galois Theory. South Bend: Notre Dame University 1955.
Artin, E.: Geometric Algebra. New York: Interscience Publishers 1957.
Artin, E. Nesbitt, E., Thrall, R.: Rings with Minimum Condition. Ann Arbor: University of Michigan Press 1944.
Bass, H.: Algebraic K-Theory. New York: Benjamin 1968.
Birkhoff, G.: Lattice Theory, Colloquium Publication, Vol. 25 (revised). Amer. Math. Soc., Providence 1948, 1967.
Bucur, I., Deleanu, A.: Introduction to the Theory of Categories and Functors. London/New York/Sidney: Interscience Publishers, Wiley 1968.
Cartan, H., Eilenberg, S.: Homological Algebra. Princeton: Princeton University Press 1956.
Chevalley, C.: Fundamental Concepts of Algebra. New York: Academic Press 1956. Clifford, A. H., Preston, G. B.: Algebraic Theory of Semigroups. Vol. 1. Surveys Amer. Math. Soc., No. 7, Providence 1961.
Cohn, P. M., Morita Equivalence and Duality. University of London, Bookstore, Queen Mary College, Mile End Road, London, 1966.
Feit, W.: Characters of Finite Groups. New York: Benjamin 1967.
Freyd, P.: Abelian Categories. New York: Harper & Row 1964.
Fuchs, L.: Abelian Groups, 2nd Ed. New York: Pergamon Press 1970. Gorenstein, D.: Finite Groups. New York: Harper & Row 1968.
Hall, M. H., Jr.: The Theory of Groups. New York: Macmillan 1959.
Herstein, I. N.: Topics in Algebra. New York: Harper & Row 1964.
Jacobson, N.: Lectures in Abstract Algebra, Vols. I — III. New York/Princeton: Van Nostrand 1951, 1953, 1964.
Jans, J.: Rings and Homology. New York: Holt, Rinehart & Winston 1964. Kaplansky, I.: Infinite Abelian Groups, 2nd Ed. Ann Arbor: University of Michigan Press 1969.
Kurosch, A.: Theory of Groups, Vols. 1 and 2. New York: Chelsea 1955, 1956.
Kurosch, A. General Algebra. New York: Chelsea 1963.
Lang, S.: Algebra. Cambridge: Addison-Wesley 1965.
MacLane, S.: Homology. Berlin/Göttingen/Heidelberg: Springer 1963.
MacLane, S. Categories for the Working Mathematician, Berlin/Heidelberg/New York: Springer 1971.
MacLane, S., Birkhoff, G.: Algebra. New York/London: MacMillan 1967.
Mitchell, B.: Theory of Categories. New York: Academic Press 1965.
Northcott, D. G.: Homological Algebra, Cambridge: Cambridge University Press 1960.
Pontry-agin, L.: Topological Groups. Princeton: Princeton University Press 1939. Rotman, J.: Theory of Groups. Boston: Allyn Bacon 1965.
Waerden, B. L. van der: Modern Algebra, Vols. 1 and 2. New York: Ungar 1948. Weyl, H.: The Classical Groups, their Invariants and Representations (revised). Princeton: Princeton University Press 1946.
Wielandt, H.: Finite Permutation Groups. New York: Academic Press 1964. Zassenhaus, H.: The Theory of Groups, 2nd Ed. New York: Chelsea 1958.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer-Verlag, Berlin · Heidelberg
About this chapter
Cite this chapter
Faith, C. (1973). Operations: Monoid, Semigroup, Group, and Category. In: Algebra. Die Grundlehren der mathematischen Wissenschaften, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80634-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-80634-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80636-0
Online ISBN: 978-3-642-80634-6
eBook Packages: Springer Book Archive