HOMOGENOUS FINITARY SYMMETRIC GROUPS


Kegel O. H. , KUZUCUOĞLU M.

INTERNATIONAL JOURNAL OF GROUP THEORY, vol.4, no.1, pp.7-12, 2015 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2015
  • Title of Journal : INTERNATIONAL JOURNAL OF GROUP THEORY
  • Page Numbers: pp.7-12

Abstract

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) .