CENTRALIZERS IN SIMPLE LOCALLY FINITE GROUPS

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KUZUCUOGLU MAHMUT

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Journal Paper

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Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2013 | Volume:2 | Issue:1 Page(s): 1-10

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Information Journal Paper

Title

CENTRALIZERS IN SIMPLE LOCALLY FINITE GROUPS

Author(s)

KUZUCUOGLU MAHMUT | Issue Writer Certificate

Keywords

CENTRALIZERQ4

INVOLUTIONQ4

LOCALLY FINITE SIMPLE GROUPQ4

Abstract

This is a survey article on centralizers of finite subgroups in locally finite, simple groups or LFS-groups as we will call them. We mention some of the open problems about centralizers of subgroups in LFS-groups and applications of the known information about the centralizers of subgroups to the structure of the locally finite group. We also prove the following: Let G be a countably in finite nonlinear LFS-group with a Kegel sequence K={(Gi, Ni) | iÎN}. If there exists an upper bound for {|Ni| | iÎN}, then for any finite semisimple subgroup F in G the subgroup CG (F) has elements of order pi for in finitely many distinct prime pi. In particular CG (F) is an in finite group. This answers Hartley’s question provided that there exists a bound on {|Ni| | iÎN}.

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APA: Copy

KUZUCUOGLU, MAHMUT. (2013). CENTRALIZERS IN SIMPLE LOCALLY FINITE GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY, 2(1), 1-10. SID. https://sid.ir/paper/212657/en

Vancouver: Copy

KUZUCUOGLU MAHMUT. CENTRALIZERS IN SIMPLE LOCALLY FINITE GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2013;2(1):1-10. Available from: https://sid.ir/paper/212657/en

IEEE: Copy

MAHMUT KUZUCUOGLU, “CENTRALIZERS IN SIMPLE LOCALLY FINITE GROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 2, no. 1, pp. 1–10, 2013, [Online]. Available: https://sid.ir/paper/212657/en

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