Definition:Index of Subgroup/Also denoted as
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Index of Subgroup: Also denoted as
Other notations seen for the index $\index G H$ of a subgroup $H$ in a group $G$ include:
- $\card {G : H}$
- $\paren {G : H}$
- $\operatorname {index} H$ (which is not recommended, as it does not indicate the group of which $H$ is a subgroup)
Some sources merely use the notation for the cardinality of the coset space and write $\card {G / H}$.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.3$. Index. Transversals
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $25$. Cyclic Groups and Lagrange's Theorem
- 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
- 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $0$: Some Conventions and some Basic Facts
- 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 $5.10$