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Centralizers of finite subgroups in Hall's universal group
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Date
2017-01-01
Author
Kegel, Otto H.
Kuzucuoğlu, Mahmut
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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 U be the Hall's universal group and F be a finite subgroup of U. Then the centralizer C-U(F) is isomorphic to an extention of Z(F) /by U.
Subject Keywords
Infinite symmetric groups
,
Universal groups
,
Centralizers of subgroups
URI
https://hdl.handle.net/11511/34747
Journal
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
DOI
https://doi.org/10.4171/rsmup/138-15
Collections
Department of Mathematics, Article
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O. H. Kegel and M. Kuzucuoğlu, “Centralizers of finite subgroups in Hall’s universal group,”
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
, pp. 283–288, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34747.