HOMOGENOUS FINITARY SYMMETRIC GROUPS

Date

2015-03-01

Author

Kegel, Otto. H.
Kuzucuoğlu, Mahmut

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We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let n be an infinite cardinal. If G = boolean OR(infinity)(i=1) G(i), where G(i), congruent to FSym(kappa(ni)), (H = boolean OR(infinity)(i=1) H-i, where H-i congruent to Alt(kappa(ni))), is a group of strictly diagonal type and xi = (p(1), p(2), ...) 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(1)p(2) ... p(i) .

Subject Keywords

Centralizer, Simple Locally Finite, Direct Limits Of Finitary Symmetric Groups

URI

https://hdl.handle.net/11511/55612

Journal

INTERNATIONAL JOURNAL OF GROUP THEORY

Collections

Department of Mathematics, Article

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Citation Formats

O. H. Kegel and M. Kuzucuoğlu, “HOMOGENOUS FINITARY SYMMETRIC GROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, pp. 7–12, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55612.