Limit Monomial Groups over Abelian Groups


BOSTAN S. , KUZUCUOĞLU M.

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, vol.44, no.6, pp.769-780, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 6
  • Publication Date: 2020
  • Title of Journal : SOUTHEAST ASIAN BULLETIN OF MATHEMATICS
  • Page Numbers: pp.769-780
  • Keywords: Monomial groups, Diagonal embedding

Abstract

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 >.