Definition:Index of Subgroup/Also defined as
Jump to navigation
Jump to search
Index of Subgroup: Also defined as
Some sources define the index $\index G H$ of a subgroup only for the case where $G$ is finite.
Some, while developing the groundwork of the subject, refer to the left index and right index, according to whether the cardinality of the left coset space or right coset space is under consideration.
However, from Left and Right Coset Spaces are Equivalent, it follows that the left index and right index are in fact the same thing, and such a distinction is of minimal relevance.
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 43$. Lagrange's theorem
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.3$: Group actions and coset decompositions
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $5$: Cosets and Lagrange's Theorem: Definition $5.10$