Definition:Hall Subgroup

Definition

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:

$\index G H \perp \order H$

Also see

• Results about Hall subgroups can be found here.

Source of Name

This entry was named for Philip Hall.

Sources

• 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