Abstract
The Wielandt subgroup ω(G) of a group G is the subgroup of elements that normalize every subnormal subgroup of G. This subgroup, now named for Wielandt, was introduced by him in 1958 [15]. For a finite non-trivial group the Wielandt subgroup is always a non-trivial, characteristic subgroup. Thus it is possible to define the ascending Wielandt series for a finite group G which terminates at the group. Write ω0(G) = 1, and for i ≥ 1, ωi(G)/ωi–1(G) = ω(G/ωi–1(G)). The smallest n such that ωn(G) = G is called the Wielandt length of G, and the class of groups of Wielandt length at most n is denoted by . From the definition it follows that is closed under homomorphic images and taking normal subgroups. Nilpotent groups in are also closed under taking subgroups.
Publisher
Cambridge University Press (CUP)
Cited by
10 articles.
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1. On theπF-norm and theH–F-norm of a finite group;Journal of Algebra;2014-03
2. On the Norm and Wielandt Series in Finite Groups;Algebra Colloquium;2012-07-05
3. On supersoluble groups of Wielandt length two;Journal of the Australian Mathematical Society;2005-06
4. Soluble Groups of Small Wielandt Length;Communications in Algebra;2004-12-29
5. The wielandt series of metabelian groups;Bulletin of the Australian Mathematical Society;2003-04