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A CONDITION IN FINITE SOLVABLE GROUPS RELATED TO CYCLIC SUBGROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  27 September 2010

D. IMPERATORE  and
MARK L. LEWIS
D. IMPERATORE*
Affiliation:
Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Università degli Studi di Napoli ‘Federico II’, Via Cinthia-I 80126, Napoli, Italy (email: diana.imperatore@unina.it)
MARK L. LEWIS
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA (email: lewis@math.kent.edu)
*
✉For correspondence; e-mail: diana.imperatore@unina.it
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Abstract

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In this paper, we classify the finite groups belonging to the class of cyclic-transitive groups. A group G is said to be cyclic-transitive if the following condition holds: if x, y, z are nonidentity elements of G such that 〈x,y〉 and 〈y,z〉 are both cyclic, then 〈x,z〉 is also cyclic.

Keywords

finite solvable groupsfinite nonsolvable groupscyclic subgroupspartitioned groups

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 267 - 272
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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