Definition:P-Group

Definition

Let $p$ be a prime integer.

A $p$-group (either finite or infinite) is a group whose elements are all $p$-elements.

Also see

• Finite Group is $p$-Group iff Order is Power of $p$

• Results about $p$-groups can be found here.

Sources

• 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 5$: Groups $\text{I}$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): $p$-group
• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $11$: The Sylow Theorems: Definition $11.8$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): $p$-group