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Space Groups and Groups of Prime Power order VII. Powerful p-Groups and Uncovered p-Groups

✍ Scribed by Mann, A.


Book ID
120091896
Publisher
Oxford University Press
Year
1992
Tongue
English
Weight
152 KB
Volume
24
Category
Article
ISSN
0024-6093

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On elements of order p in powerful p-gro
✍ L. HΓ©thelyi; L. LΓ©vai πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 159 KB

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