Limit Monomial Groups over Abelian Groups


BOSTAN S. , KUZUCUOĞLU M.

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, cilt.44, ss.769-780, 2020 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 44 Konu: 6
  • Basım Tarihi: 2020
  • Dergi Adı: SOUTHEAST ASIAN BULLETIN OF MATHEMATICS
  • Sayfa Sayıları: ss.769-780

Özet

O. Ore in 1942 proved that for a finite degree monomial group over an abelian group H, the quotient B(n, H)/B-0(n, H) is isomorphic to H. Here we show that, even for infinite cyclic group C, if the degree lambda is an infinite Steinitz number, then B (lambda, C)/B-0(lambda, C) is not necessarily isomorphic to C. In fact we classify all these groups with respect to the characteristic lambda, namely: B (lambda, C)/B-0(lambda, C) is isomorphic to the subgroup Q(lambda) of additive group of rational numbers where Q(lambda) = < 1/p(tp) vertical bar 0 <= t(p) <= r(p), p vertical bar lambda >.