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On locally finite k-homogeneous permutation groups

โœ Scribed by M. Yoshizawa


Publisher
Springer
Year
2002
Tongue
English
Weight
197 KB
Volume
79
Category
Article
ISSN
0003-889X

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A permutation group G is said to be a group of finite type {k}, k a positive integer, if each nonidentity element of G has exactly k fixed points. We show that a group G can be faithfully represented as an irredundant permutation group of finite type if and only if G has a non-trivial normal partiti

On Centralizers in Locally Finite Groups
โœ Pavel Shumyatsky ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 76 KB

The main result of the paper is the following theorem. Let G be a locally finite group containing a finite p-subgroup A such that C G A is finite and a non-cyclic subgroup B of order p 2 such that C G b has finite exponent for all b โˆˆ B # . Then G is almost locally solvable and has finite exponent.