JournalsrsmupVol. 138pp. 283–288

Centralizers of finite subgroups in Hall’s universal group

  • Otto H. Kegel

    Universität Freiburg, Germany
  • Mahmut Kuzucuoğlu

    Middle East Technical University, Ankara, Turkey
Centralizers of finite subgroups in Hall’s universal group cover
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Abstract

The structure of the centralizers of elements and finite abelian subgroups in Hall's universal group is studied by B. Hartley by using the property of existential closed structure of Hall’s universal group in the class of locally finite groups. The structure of the centralizers of arbitrary finite subgroups were an open question for a long time. Here by using basic group theory and the construction of P. Hall we give a complete description of the structure of centralizers of arbitrary finite subgroups in Hall's universal group. Namely we prove the following. Let UU be the Hall's universal group and FF be a finite subgroup of UU.Then the centralizer CU(F)C_U(F) is isomorphic to an extention of Z(F)Z(F) by UU.

Cite this article

Otto H. Kegel, Mahmut Kuzucuoğlu, Centralizers of finite subgroups in Hall’s universal group. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 283–288

DOI 10.4171/RSMUP/138-15