HOMOGENOUS FINITARY SYMMETRIC GROUPS

Kegel O. H., KUZUCUOĞLU M.

INTERNATIONAL JOURNAL OF GROUP THEORY, cilt.4, sa.1, ss.7-12, 2015 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Sayı: 1
  • Basım Tarihi: 2015
  • Dergi Adı: INTERNATIONAL JOURNAL OF GROUP THEORY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.7-12
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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) .