In this paper we study the structure of locally solvable, solvable, locally nilpotent, and nilpotent maximal subgroups of skew linear groups. In [S. Akbari et al., J. Algebra 217 (1999) 422–433] it has been conjectured that if D is a division ring and M a nilpotent maximal subgroup of D∗, then D is commutative. In connection with this conjecture we show that if F [M]\F contains an algebraic ele...

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in maximal group. classify groups, and their subgroups rational points, up to conjugacy by birational map.

Let G be a finite p-group which has exactly one maximal subgroup H such that |H| > p. Then we have d(G) = 2, p = 2, H is a four-group, G is abelian of order 8 and type (4, 2), G is of class 3 and the structure of G is completely determined. This solves the problem Nr. 1800 stated by Y. Berkovich in [3]. We consider here only finite p-groups and our notation is standard (see [1]). If G is a p-gr...

We are concerned with conditions under which a locally compact group G has a maximal compact normal subgroup K and whether or not G/K is a Lie group. If G has small compact normal subgroups K such that G/K is a Lie group, then G is pro-Lie. If in G there is a collection of closed normal subgroups {Ha} such that f~| Ha = e and G/Ha is a Lie group for each a, then G is a residual Lie group. We de...

We classify pairs (X,G) consisting of a complex K3 surface X and finite group G≤Aut(X) such that the subgroup G s ⪇G symplectic automorphisms is among 11 maximal ones as classified by Mukai.

We show that, for the O'Nan sporadic simple group, there is no Rwpri and (IP)2 geometry of rank 6 with a maximal parabolic subgroup isomorphic to M11 and that there is no Rwpri and (IP)2 geometry of rank 5 with a maximal parabolic subgroup isomorphic to J1 . This last result permits us to show that the Ivanov Shpectorov geometry is not Rwpri. The results obtained in this paper rely partially on...

This paper and its sequel [17] deal with a range of questions about the subgroup structure of infinite symmetric groups. Our concern is with such questions as the following. How can an infinite symmetric group be expressed as the union of a chain of proper subgroups? What are the subgroups that supplement the normal subgroups of an infinite symmetric group? What are the maximal proper subgroups...

Let [Formula: see text] be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if normal subgroup group then the image an text]-maximal in not, general, text]. We say reduction text]-theorem holds for if, every extension (i.e. contains as subgroup), number conjugacy classes subgroups same. The implies In this paper, we prove only all are c...