1 results
ON THE
$p$-LENGTH AND THE WIELANDT SERIES OF A FINITE 
$p$-SOLUBLE GROUP
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 09 December 2014, pp. 219-226
- Print publication:
- April 2015
-
- Article
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- You have access
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The Wielandt subgroup of a group
$G$, denoted by 
${\it\omega}(G)$, is the intersection of the normalisers of all subnormal subgroups of 
$G$. The terms of the Wielandt series of 
$G$ are defined, inductively, by putting 
${\it\omega}_{0}(G)=1$ and 
${\it\omega}_{i+1}(G)/{\it\omega}_{i}(G)={\it\omega}(G/{\it\omega}_{i}(G))$. In this paper, we investigate the relations between the
$p$-length of a 
$p$-soluble finite group and the Wielandt series of its Sylow 
$p$-subgroups. Some recent results are improved.
