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On elements of order p in powerful p-groups

✍ Scribed by L. Héthelyi; L. Lévai

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
159 KB
Volume
270
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 such that Ω 1 (P ) is not of exponent 2.

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