centralizers in simple locally finite groups
نویسندگان
چکیده
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 infinite non-linear lfs-group with a kegel sequence $mathcal{k}={(g_i,n_i) | iin mathbf{n} }$. if there exists an upper bound for ${ |n_i| | iin mathbf{n} }$, then for any finite semisimple subgroup $f$ in $g$ the subgroup $c_g(f)$ has elements of order $p_i$ for infinitely many distinct prime $p_i$. in particular $c_g(f)$ is an infinite group. this answers hartley's question provided that there exists a bound on ${ |n_i| | iin mathbf{n} }.$
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عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 2
شماره 1 2012
کلمات کلیدی
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