Abstract
Dimension subgroups in characteristic p are employed in the study of the power structure of finite p-groups. We show, e.g., that if G is a p-group of class c (p odd) and k={top left corner}log p ((c+1)/(p-1)){top right corner}, then, for all i, any product of p i+k th powers in G is a p i th power. This sharpens a previous result of A. Mann. Examples are constructed in order to show that our constant k is quite often the best possible, and in any case cannot be reduced by more than 1.
Original language | American English |
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Pages (from-to) | 45-56 |
Number of pages | 12 |
Journal | Israel Journal of Mathematics |
Volume | 73 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1991 |
Externally published | Yes |