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Homogenous finitary symmetric groups | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 4، شماره 1، خرداد 2015، صفحه 7-12 اصل مقاله (387.69 K) | ||
| نوع مقاله: Ischia Group Theory 2014 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2015.7277 | ||
| نویسندگان | ||
| Otto. H. Kegel1؛ Mahmut Kuzucuoğlu* 2 | ||
| 1Mathematisches Institut Albert Ludwigs Universitat Eckerstr | ||
| 2Middle East Technical University | ||
| چکیده | ||
| We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let $\kappa$ be an infinite cardinal. If $G=\underset{i=1}{\stackrel{\infty}\bigcup} G_i$, where $G_i\cong FSym(\kappa n_i)$, ($H=\underset{i=1}{\stackrel{\infty}\bigcup}H_i$, where $H_i\cong Alt(\kappa n_i)$), is a group of strictly diagonal type and $\xi=(p_1, p_2, \ldots )$ is an infinite sequence of primes, then $G$ is isomorphic to the homogenous finitary symmetric group $FSym(\kappa)(\xi)$ ($H$ is isomorphic to the homogenous alternating group $Alt(\kappa)(\xi))$, where $n_0=1$, $n_i=p_1p_2\cdots p_i$. | ||
| کلیدواژهها | ||
| Finitary symmetric groups؛ Centralizer؛ Locally finite simple groups | ||
| مراجع | ||
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N. R. Brumberg (1963) Bond of wreath products with other operations on groups Siberian Math. J. 4, 1221-1234
R. G. Burns (1968) A wreath tower construction of countably infinite locally finite groups Math. Zeitschr. 105, 367-386
U. B. Guven, O. H. Kegel and M. Kuzucuoglu (2015) Centralizers of subgroups in direct limits of symmetric
groups with strictly diagonal embedding Comm. Algebra. 43 (6), 1-15
J. D. Dixon and B. Mortimer (1996) Permutation groups}, Graduate Texts in Mathematics Springer -Verlag, New York 163
N. V. Kroshko and V. I. Sushchansky (1998) Direct Limits of symmetric and alternating groups with strictly diagonal
embeddings Arch. Math. (Basel) 71, 173-182
Ya. V. Lavrenyuk and V. I. Sushchansky Automorphisms of homogeneous symmetric groups and
hierarchomorphisms of rooted trees Algebra Discrete Math. 2003 (4), 33-49
J. D. P. Meldrum (1995) Wreath products of groups and semigroups}, Pitman Monographs and Surveys in Pure and Applied Mathematics Longman, Harlow 74
A. E. Zalesskii (1998) Direct limits of finite dimensional algebras and finite groups Canadian Mathematical Society, Conference proceeding 22, 221-239
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