On certain minimal non--groups for some classes


ARIKAN A. , ERCAN S.

TURKISH JOURNAL OF MATHEMATICS, cilt.39, sa.4, ss.564-569, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 39 Konu: 4
  • Basım Tarihi: 2015
  • Doi Numarası: 10.3906/mat-1406-31
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.564-569

Özet

Let {theta(n)}(infinity)(n=1) be a sequence of words. If there exists a positive integer n such that theta(m)(G) = 1 for every m >= n, then we say that G satisfies (*) and denote the class of all groups satisfying (*) by x{theta(n)}(infinity)(n=11)is. If for every proper subgroup K of G, K is an element of x{theta(n)} but G is not an element of{theta(n)}(infinity)(n=11), then we call G a minimal non-x{theta(n)}(infinity)(n=1),-group. Assume that G is an infinite locally finite group with trivial center and theta(i)(G) = G for all i >= 1. In this case we mainly prove that there exists a positive integer t such that for every proper normal subgroup N of G, either theta(t)(N) = 1 or theta(t)(CG(N)) = 1. We also give certain useful applications of the main result.