2 results
ON THE
$p$-LENGTH AND THE WIELANDT SERIES OF A FINITE 
$p$-SOLUBLE GROUP
- Part of
-
- 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
-
- You have access
- Export citation
-
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.
ON THE
$p$-LENGTH AND THE WIELANDT LENGTH OF A FINITE 
$p$-SOLUBLE GROUP
- Part of
-
- 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
-
- You have access
- Export citation
-
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.
