This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Adian, The Burnside problem and identities in groups, trans. John Lennox and James Wiegold, Springer-Verlag, Berlin, New York, 1979.
J.L. Alperin, "Automorphisms of solvable groups", Proc. Amer. Math. Soc. 13 (1962), 175–180.
A.O. Asar, "On a problem of Kegel and Wehrfritz", J. Algebra 59 (1979), 47–55.
A.O. Asar, "The solution of a problem of Kegel and Wehrfritz", Proc. London Math. Soc. (3) 45 (1982), 337–364.
V.V. Belyaev and N.F. Sesekin, "Periodic groups with an almost regular involutive automorphism," Studia Sci. Math. Hungar. 17 (1982), 137–141.
A.V. Borovik, "Embeddings of finite Chevalley groups and periodic linear groups," Sibirsk. Mat. Zh. 24 (1983), 26–35 (Russian) = Siberian Math. J. 24 (1983), 843–55.
P. Fong, "On orders of finite groups and centralizers of p-elements," Osaka J. Math. 13 (1976), 483–489.
P. Hall, "A contribution to the theory of groups of prime power order," Proc. London Math. Soc. (2) 36 (1934), 29–95.
P. Hall and C.R. Kulatilaka, "A property of locally finite groups," J. London Math. Soc. 39 (1964), 235–239.
B. Hartley and Th. Meixner, "Periodic groups in which the centralizer of an involution has bounded order," J. Algebra 64 (1980), 285–291.
B. Hartley, Centralizers in locally finite groups, Lecture Notes No. 12, Department of Mathematics, National University of Singapore, 1982.
B. Hartley and Th. Meixner, "Finite soluble groups in which the centralizer of an element of prime order is small," Arch. Math. 36 (1981), 211–213.
B. Hartley, "Periodic locally soluble groups containing an element of prime order with Černikov centralizer," Quart. J. Math. Oxford (2) 33 (1982), 309–323.
B. Hartley and G. Shute, "Monomorphisms and direct limits of finite groups of Lie type," Quart. J. Math. Oxford (2) 35 (1984), 49–71.
B. Hartley, "Fixed points of automorphisms of prime power order of locally finite groups and Chevalley groups", in preparation.
B. Hartley, Topics in the theory of nilpotent groups, in Group Theory. Essays for Philip Hall (Academic Press, London, 1984).
G. Higman, "Groups and rings having automorphisms without non-trivial fixed points," J. London Math. Soc. 32 (1957), 321–334.
E.I. Huhro, "Finite p-groups admitting an automorphism of order p with a small number of fixed points," Mat. Zametki 38 (1985), 652–657 (Russian).
M.I. Kargapolov, "On the problem of O. Yu. Šmidt, Sibirsk. Mat. Zh. 4 (1963), 233–235.
O.H. Kegel and B.A.F. Wehrfritz, Locally finite groups (North Holland, Amsterdam, 1973).
O.H. Kegel and B.A.F. Wehrfritz, "Strong finiteness conditions in locally finite groups," Math. Z. 117 (1970), 309–324.
Th. Meixner, Uber endliche Gruppen mit Automorphismen, deren Fixpunktgruppe beschränkt sind (Doctoral thesis, Universität Erlangen-Nürnberg, 1979).
Th. Meixner, "Metabelsche Gruppen mit einem fixpunktfreien Automorphismus von Primzahlordnung," Arch. Math. 35 (1980), 497–500.
Th. Meixner, "Solvable groups admitting an automorphism of prime power order whose centralizer is small," J. Algebra 99 (1986), 181–190.
I.I. Pavlyuk, "On a problem of Kegel and Wehrfritz", Proc. Seventh All-Union Symposium on Group Theory, Krasnoyarsk, 1980.
A.A. Šafiro and V.P. Šunkov, "Locally finite groups with Černikov centralizers of involutions," in Studies in Group Theory, Inst. Fiz. im Kirenskogo Sibirsk. Otdel Akad. Nauk SSSR, Krasnoyarsk, 1975.
A.A. Šafiro and V.P. Šunkov, "A characterization of an infinite Černikov group which is not a finite extension of a quasicyclic group," Mat. Sb. (N.S.) 107 (149)(1978), 289–303.
R. Steinberg, Endomorphisms of algebraic groups, Mem. Amer. Math. Soc. 80 (1968).
V. Stingl and V. Turau, "Locally finite Syl*p-groups," J. Algebra 90 (1984), 354–363.
V.P. Šunkov, "On the minimality problem for locally finite groups," Algebra i Logika 9 (1970), 220–248 (Russian) = Algebra and Logic 9 (1970), 137–151.
V.P. Šunkov, "On periodic groups with an almost regular involution," Algebra i Logika 11 (1972), 470–493 (Russian) = Algebra and Logic 11 (1972), 260–272.
Simon Thomas, "An identification theorem for the locally finite nontwisted Chevalley groups," Arch. Math. 40 (1983), 21–31.
Simon Thomas, "The classification of the simple periodic linear groups," Arch. Math. 41 (1983), 103–116.
V. Turau, "Zentralisatoren in lokal-endlichen Gruppen vom Chevalley-Typ," Arch. Math. 44 (1985), 297–308.
J.S. Wilson, "On groups satisfying Min-p," Proc. London Math. Soc. (3) 26 (1973), 226–248.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Hartley, B. (1987). Centralizers in locally finite groups. In: Kegel, O.H., Menegazzo, F., Zacher, G. (eds) Group Theory. Lecture Notes in Mathematics, vol 1281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078689
Download citation
DOI: https://doi.org/10.1007/BFb0078689
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18399-0
Online ISBN: 978-3-540-47948-2
eBook Packages: Springer Book Archive