Geodesic
ON THE CENTRALIZER OF AN ELEMENT OF ORDER FOUR IN A LOCALLY FINITE GROUP
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 411-415

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that if G is a locally finite group admitting an automorphism φ of order four such that C G (φ) is Chernikov, then G has a soluble subgroup of finite index. 
SHUMYATSKY, PAVEL. ON THE CENTRALIZER OF AN ELEMENT OF ORDER FOUR IN A LOCALLY FINITE GROUP. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 411-415. doi: 10.1017/S0017089507003746
@article{10_1017_S0017089507003746,
     author = {SHUMYATSKY, PAVEL},
     title = {ON {THE} {CENTRALIZER} {OF} {AN} {ELEMENT} {OF} {ORDER} {FOUR} {IN} {A} {LOCALLY} {FINITE} {GROUP}},
     journal = {Glasgow mathematical journal},
     pages = {411--415},
     year = {2007},
     volume = {49},
     number = {2},
     doi = {10.1017/S0017089507003746},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003746/}
}
TY  - JOUR
AU  - SHUMYATSKY, PAVEL
TI  - ON THE CENTRALIZER OF AN ELEMENT OF ORDER FOUR IN A LOCALLY FINITE GROUP
JO  - Glasgow mathematical journal
PY  - 2007
SP  - 411
EP  - 415
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003746/
DO  - 10.1017/S0017089507003746
ID  - 10_1017_S0017089507003746
ER  - 
%0 Journal Article
%A SHUMYATSKY, PAVEL
%T ON THE CENTRALIZER OF AN ELEMENT OF ORDER FOUR IN A LOCALLY FINITE GROUP
%J Glasgow mathematical journal
%D 2007
%P 411-415
%V 49
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003746/
%R 10.1017/S0017089507003746
%F 10_1017_S0017089507003746

[1] 1. Asar, A. O., The solution of a problem of Kegel and Wehrfritz, Proc. London Math. Soc. (3) 45 (1982), 337–364. Google Scholar | DOI

[2] 2. Feit, W. and Thompson, J., Solvability of groups of odd order, Pacific J. Math. 13 (1963), 773–1029. Google Scholar

[3] 3. Gorenstein, D., Finite groups (Harper and Row, New York, 1968). Google Scholar

[4] 4. Hartley, B., Fixed points of automorphisms of certain locally finite groups and Chevalley groups, J. London Math. Soc. (2) 37 (1988), 421–436. Google Scholar | DOI

[5] 5. Hartley, B., A general Brauer-Fowler theorem and centralizers in locally finite groups, Pacific J. Math. 152 (1992), 101–117. Google Scholar | DOI

[6] 6. Higman, G., Groups and Lie rings having automorphisms without non-trivial fixed points, J. London Math. Soc. 32 (1957), 321–334. Google Scholar | DOI

[7] 7. Kegel, O. H. and Wehrfritz, B. A. F., Strong finiteness conditions in locally groups, Math. Z. 117 (1970), 309–324. Google Scholar | DOI

[8] 8. Kegel, O. H. and Wehrfritz, B. A. F., Locally finite groups (North Holland, Amsterdam, 1973). Google Scholar

[9] 9. Khukhro, E. I., Groups and Lie rings admitting an almost regular automorphism of prime order, Math. USSR Sbornik 71 (1992), 51–63. Google Scholar | DOI

[10] 10. Khukhro, E. I. and Makarenko, N. Yu., Large characteristic subgroups satisfying multilinear commutator identities, J. London Math. Soc. to appear. Google Scholar

[11] 11. Kovács, L., Groups with regular automorphisms of order four, Math. Z. 75 (1961), 277–294. Google Scholar | DOI

[12] 12. Kreknin, V. A., Solvability of Lie algebras with a regular automorphism of finite period, Soviet Math. Dokl. 4 (1963), 683–685. Google Scholar

[13] 13. Kreknin, V. A. and Kostrikin, A. I., Lie algebras with regular automorphisms, Soviet Math. Dokl. 4 (1963), 355–358. Google Scholar

[14] 14. Kurzweil, H., p-Automorphismen von auflösbaren p-Gruppen, Math. Z. 120 (1971), 326–354. Google Scholar | DOI

[15] 15. Yu, N.. Makarenko, Finite 2-groups admitting an automorphism of order 4 with few fixed points, Algebra and Logic 32 (1993), 215–230. Google Scholar

[16] 16. Yu, N.. Makarenko, Finite 2-groups with an automorphism of order 4, Algebra and Logic 40 (2001), 47–54. Google Scholar

[17] 17. Makarenko, N. Yu. and Khukhro, E. I., Lie rings with automorphisms of degree 4 with small number of fixed points, Algebra and Logic 35 (1996), 21–43. Google Scholar | DOI

[18] 18. Makarenko, N. Yu. and Khukhro, E. I., Nilpotent groups admitting an almost regular automorphism of order 4 Algebra and Logic 35 (1996), 176–187. Google Scholar | DOI

[19] 19. Makarenko, N. Yu. and Khukhro, E. I., Lie rings admitting an automorphism of order 4 with few fixed points II, Algebra and Logic 37 (1998), 78–91. Google Scholar | DOI

[20] 20. Makarenko, N. Yu. and Khukhro, E. I., Finite groups with an almost regular automorphism of order four, Algebra and Logic 45 (2006), 326–343. Google Scholar | DOI

[21] 21. Shumyatsky, P., On locally finite groups admitting an automorphism of prime order whose centralizer is Chernikov, Houston J. Math. 20 (1994), 187–192. Google Scholar

[22] 22. Shunkov, V. P., On the minimality problem for locally finite groups, Algebra and Logic 9 (1970), 137–151. Google Scholar | DOI

[23] 23. Thompson, J. G., Finite groups with fixed-point-free automorphisms of prime order, Proc. Nat. Acad. Sci. USA 45 (1959), 578–581. Google Scholar PubMed | DOI

[24] 24. Thompson, J. G., Automorphisms of solvable groups, J. Algebra 1 (1964), 259–267. Google Scholar | DOI

[25] 25. Turau, V., Zentralisatoren in lokal-endlichen Gruppen vom Chevalley-Typ, Arch. Math. (Basel) 44 (1985), 297–308. Google Scholar | DOI

Cité par Sources :