Abstract
In this paper, we study the structure of locally generalized radical subgroups of the general skew linear group GLn(D) of degree n ≥ 1 over a division ring D. Among results, we show that if G is a locally generalized radical almost subnormal subgroup of GLn(D), then G is central provided D is not a locally finite field in case n ≥ 2 and D is weakly locally finite in case n = 1. Also, we prove that if G is a generalized radical almost subnormal subgroup of the multiplicative group D⁎, then G is central. We also prove that every generalized radical ascendant subgroup of GLn(D) is central provided D is not a locally finite field in case n ≥ 2 and D is any division ring in case n = 1. Finally, we show that if D is a locally finite division ring, then every locally generalized radical ascendant subgroup of the group D⁎ is central.
Le, V.C. and Bui, X.H. (2026) Journal of Algebra, 697, pp. 854–873.