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Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Then $H$ is a Hall subgroup of $G$ if and only if the index and order of $H$ in $G$ are coprime:
- $\index G H \perp \order H$
- Results about Hall subgroups can be found here.
Source of Name
This entry was named for Philip Hall.
- 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Hall subgroup