Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T05:02:39.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal complements in finite solvable groups

Published online by Cambridge University Press:  09 April 2009

Donald K. Friesen
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A well known theorem ([1] page 432) in the study of finite groups states that if P is a Sylow p-subgroup of the finite group G, and if P0 is a normal subgroup of P such that whenever two elements, σ and τ, of P are conjugate in G, the cosets σP0 and τP0 are conjugate in P/P0, then there is a normal subgroup K of G such that G = KP and K ∩ P = P0. In this note we will extend this result to allow P to be any Hall subgroup if G is solvable. More precisely, following theorem will be the proved.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 262 - 264
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Huppert, B., Endliche Gruppen (Springer-Verlag, 1967).CrossRefGoogle Scholar