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ON THE
$p$-LENGTH AND THE WIELANDT LENGTH OF A FINITE 
$p$-SOLUBLE GROUP
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 88 / Issue 3 / December 2013
- Published online by Cambridge University Press:
- 07 March 2013, pp. 453-459
- Print publication:
- December 2013
-
- Article
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The
$p$-length of a finite 
$p$-soluble group is an important invariant parameter. The well-known Hall–Higman 
$p$-length theorem states that the 
$p$-length of a 
$p$-soluble group is bounded above by the nilpotent class of its Sylow 
$p$-subgroups. In this paper, we improve this result by giving a better estimation on the 
$p$-length of a 
$p$-soluble group in terms of other invariant parameters of its Sylow 
$p$-subgroups.
