Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-24T12:49:20.856Z Has data issue: false hasContentIssue false

A note on subnormal defect in finite soluble groups

Published online by Cambridge University Press:  17 April 2009

R.A. Bryce
Affiliation:
Department of Mathematics, Faculty of Science, Australian National University, Canberra, A.C.T. 2601, Australia.
Rights & Permissions [Opens in a new window]

Abstract

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.

It is shown that for every positive integer n there exists a finite group of derived length n in which all Sylow subgroups are abeian and in which the defect of subnormal subgroups is at most 3.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Casolo, C., ‘Gruppi finiti risolubili in cui tutti i sottogruppi subnormali hanno difetto al più due’, Rend. Sem. Mat. Univ. Padova 71 (1984), 257271.Google Scholar
[2]Casolo, C., ‘Groups with subnormal subgroups of bounded defect’, Rend. Sem. Mat. Univ. Padova 77 (1987), 177187.Google Scholar
[3]Cossey, John, Groups of odd order in which every subnormal subgroup has defect at most two (MSRC Research Report No. 35, Department of Mathematics, Faculty of Science, ANU. Canberra, 1987).Google Scholar
[4]Gaschütz, W., ‘Gruppen in denen des Normalteilersein transitiv ist’, J. Reine Angew. Math. 198 (1957), 8792.CrossRefGoogle Scholar
[5]Hawkes, T., ‘Groups whose subnormal subgroups have bounded defect’, Arch. Math. 43 (1984), 289294.CrossRefGoogle Scholar
[6]McCaughan, D. and Stonehewer, S., ‘Finite soluble groups whose subnormal subgroups have defect at most 2’, Arch. Math. 35 (1980), 5660.CrossRefGoogle Scholar
[7]Zacher, G., ‘Caratterizzazione dci t-gruppi finiti risolubili’, Ricerche Mat. 1 (1952), 287294.Google Scholar