ON SOME SUBGROUPS OF D^*WHICH SATISFY A GENERALIZED GROUP IDENTITY

Abstract

Abstract. Let D be a division ring and w(x 1 , x 2 , . . . , xm) be a generalized group monomial over D * . In this paper, we investigate subnormal subgroups and maximal subgroups of D * which satisfy the identity w(x 1 , x 2 , . . . , xm) = 1.

Về đồng nhất thức nhóm suy rộng của nhóm tuyến tính tổng quát trên vành chia có tâm hữu hạn

“…Chứng minh. Xem bài báo (Bien, 2015). Do Mệnh đề 2.1. đúng với mọi không gian vectơ phải V nên kể từ đây ta luôn xem…”

Free subgroups in almost subnormal subgroups of general skew linear groups

“…which is a generalized group monomial over G by [3,Lemma 3.2]. Since H r is normal in H r−1 , c i ac…”

“…Theorem 3.3 no longer holds if D is a finite field. Indeed, let D = F q be a finite field with q elements and consider the projective special linear group PSL(n, q) which is different from the groups PSL(2, 2) and PSL (2,3). Then, it is well-known that PSL(n, q) is a simple group.…”