✦ LIBER ✦

On Groups of Order p q

✍ Scribed by Burnside, W.

Book ID: 120104148
Publisher: Oxford University Press
Year: 1904
Tongue: English
Weight: 159 KB
Volume: s2-1
Category: Article
ISSN: 0024-6115
DOI: 10.1112/plms/s2-1.1.388

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We investigate the set Ω {1} (P ) of elements of order at most p in a powerful p-group P and prove that |Ω {1} (P )| = |P : P p |. As a corollary, we obtain a necessary and sufficient condition for Ω 1 (P ) to be of exponent p. We give an example to show that for p = 2 there is a powerful 2-group su