Polynomial identities and maximal subgroups of skew linear groups

Kiani, Dariush

doi:10.1007/s00229-007-0124-0

Cited by 7 publications

(2 citation statements)

References 10 publications

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“…Some properties of maximal subgroups of GL n D have been studied in a series of articles, see, e.g., [7][8][9]. Recall that a group G is an FC-group if every element of G has only a finite number of conjugates.…”

Section: Introductionmentioning

confidence: 99%

Maximal Subgroups of Subnormal Subgroups ofGL_n(D) with Finite Conjugacy Classes

Kiani¹,

Ramezan-Nassab²

2010

Communications in Algebra

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Let D be an infinite division ring. A famous result due to Herstein says that every noncentral element of D has infinitely many conjugates in D. So, if D * is an FC-group, then D is a field. Now let N be a subnormal subgroup of GL n D , where n ≥ 1, and M a maximal subgroup of N . In this article, we prove that if M is an FC-group, then M is contained in the multiplicative group of some subfield of M n D .

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Section: Introductionmentioning

confidence: 99%

Maximal Subgroups of Subnormal Subgroups ofGL_n(D) with Finite Conjugacy Classes

Kiani¹,

Ramezan-Nassab²

2010

Communications in Algebra

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“…In section 2, instead of maximal subgroups of GL n (D), we consider maximal subgroups of subnormal subgroups of GL n (D). The structure of such groups have been investigated in various papers, see, e.g., [6,8,12,14]. As mentioned earlier, if D is an infinite division ring, in [3] it was shown that every nilpotent maximal subgroup of GL n (D) is abelian.…”

Section: Introductionmentioning

confidence: 99%

Nilpotent and polycyclic-by-finite maximal subgroups of skew linear groups

Ramezan-Nassab

Kiani

2014

Journal of Algebra

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Let D be an infinite division ring, n a natural number and N a subnormal subgroup of GL n (D) such that n = 1 or the center of D contains at least five elements. This paper contains two main results. In the first one we prove that each nilpotent maximal subgroup of N is abelian; this generalizes the result in [R. Ebrahimian, J. Algebra 280 (2004) 244-248] (which asserts that each maximal subgroup of GL n (D) is abelian) and a result in [M. Ramezan-Nassab, D. Kiani, J. Algebra 376 (2013) 1-9]. In the second one we show that a maximal subgroup of GL n (D) cannot be polycyclic-by-finite.

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