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ON SOLUBILITY OF GROUPS WITH FEW NORMALISERS

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  12 May 2014

MOHAMMAD ZARRIN
MOHAMMAD ZARRIN*
Affiliation:
Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran email [email protected], [email protected]
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Abstract

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In this paper we prove that every group with at most 26 normalisers is soluble. This gives a positive answer to Conjecture 3.6 in the author’s paper [On groups with a finite number of normalisers’, Bull. Aust. Math. Soc.86 (2012), 416–423].

Keywords

normaliser subgroupssimple groupssoluble groups

MSC classification

Secondary: 20E34: General structure theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 247 - 249
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Camp-Mora, S., ‘Locally finite groups with two normalizers’, Comm. Algebra 28 (2000), 5475–5480.CrossRefGoogle Scholar
Heineken, H., ‘A class of three-Engel groups’, J. Algebra 17 (1971), 341–345.Google Scholar
Mahdavianary, S. K., ‘A special class of three-Engel groups’, Arch. Math. 40 (1983), 193–199.CrossRefGoogle Scholar
Newman, M. F., ‘The soluble length of soluble linear groups’, Math. Z. 126 (1972), 59–70.CrossRefGoogle Scholar
Pérez-Ramos, M. D., ‘Groups with two normalizers’, Arch. Math. 50 (1988), 199–203.CrossRefGoogle Scholar
Tota, M., ‘Groups with a finite number of normalizer subgroups’, Comm. Algebra 32 (2004), 4667–4674.CrossRefGoogle Scholar
Zarrin, M., ‘On groups with a finite number of normalisers’, Bull. Aust. Math. Soc. 86 (2012), 416–423.CrossRefGoogle Scholar