Category:Examples of Use of Lagrange's Theorem (Group Theory)
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This category contains examples of Lagrange's Theorem (Group Theory).
Let $G$ be a finite group.
Let $H$ be a subgroup of $G$.
Then:
- $\order H$ divides $\order G$
where $\order G$ and $\order H$ are the order of $G$ and $H$ respectively.
In fact:
- $\index G H = \dfrac {\order G} {\order H}$
where $\index G H$ is the index of $H$ in $G$.
When $G$ is an infinite group, we can still interpret this theorem sensibly:
- A subgroup of finite index in an infinite group is itself an infinite group.
- A finite subgroup of an infinite group has infinite index.
Pages in category "Examples of Use of Lagrange's Theorem (Group Theory)"
The following 4 pages are in this category, out of 4 total.
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- Lagrange's Theorem (Group Theory)/Examples
- Lagrange's Theorem (Group Theory)/Examples/Intersection of Subgroups of Order 25 and 36
- Lagrange's Theorem (Group Theory)/Examples/Order of Group with Subgroups of Order 25 and 36
- Lagrange's Theorem (Group Theory)/Examples/Order of Union of Subgroups of Order 16