Applications of dimension subgroups to the power structure of p-groups

Carlo M. Scoppola*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageAmerican English
Pages (from-to)45-56
Number of pages12
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Feb 1991
Externally publishedYes


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