Maximal subgroups of the Coxeter group W(H4) and quaternions

The largest finite subgroup of O(4) is the non-crystallographic Coxeter group W(H₄) of order 14,400. Its derived subgroup is the largest finite subgroup W(H₄)/Z₂ of SO(4) of order 7200. Moreover, up to conjugacy, it has five non-normal maximal subgroups of orders 144, two 240, 400 and 576. Two groups [W(H₂) × W(H₂)] ⋊ Z₄ and W(H₃) × Z₂ possess non-crystallographic structures with orders 400 and 240 respectively. The groups of orders 144, 240 and 576 are the extensions of the Weyl groups of the root systems of SU(3) × SU(3), SU(5) and SO(8) respectively. We represent the maximal subgroups of W(H₄) with sets of quaternion pairs acting on the quaternionic root systems.     

The maximal subgroups of F4(2) and its automorphism group

We completely determine the conjugacy classes of maximal subgroups of the finite simple group F₄(2) of Lie type, and of its automorphism group.     

Certain discrete subgroups in the exceptional group G2(C) in connection with Eisenstein series

In the paper one proves several statements on congruence subgroups in the exceptional Lie group G ₂ (C). having applications in the theory of automorphic functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 183, pp. 124–141, 1990.     

Systems of generators of subgroups of PSL(2,C)

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 191–193, January–February, 1990.     

Remarks on points of approximation of discrete subgroups of U(1,n; C)

In the study of a geometrically finite kleinian group, the properties of points of approximation are discussed (see [2]). We show that ifG is a discrete subgroup ofU(1, n; C) acting on the complex unit ballB ⁿ, then a point of approximation ofG has similar properties as in a kleinian group. In the case wheren>-2, however, an approach to a point of approximation is not necessarily non-tangential. We shall give an example of a point of approximation to which some orbit converges in the tangential direction. Dedicated to Professor Nobuyuki Suita on his sixtieth birthday     

On three color Ramsey numbers R(C4,C4,K1,n)

For $k$ given graphs $G_1,G_2,\dots ,G_k$, $k\ge 2$, the $k$-color Ramsey number, denoted by $R(G_1,G_2,\dots ,G_k)$, is the smallest integer $N$ such that if we arbitrarily color the edges of a complete graph of order $N$ with $k$ colors, then it always contains a monochromatic copy of $G_i$ colored with $i$, for some $1\le i\le k$. Let $C_m$ be a cycle of length $m$ and $K_{1,n}$ a star of order $n+1$. In this paper, firstly we give a general upper bound of $R(C_4,C_4,\dots ,C_4,K_{1,n})$. In particular, for the 3-color case, we have $R(C_4,C_4,K_{1,n})\le n+?\sqrt{4n+5}?+3$ and this bound is tight in some sense. Furthermore, we prove that $R(C_4,C_4,K_{1,n})\le n+?\sqrt{4n+5}?+2$ for all $n={?}^2??$ and $?\ge 2$, and if $?$ is a prime power, then the equality holds.     

A finiteness theorem for subgroups of SP (4,Z)

This paper proves that there are only finitely many subgroupsH of finite index in Sp(4,Z) such that coresponding quotient of the Siegel upper half space of rank two is not of general type. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. vol. 56. Algebraic Geometry-9, 1998.     

A class of 2-generator subgroups of PSL (2, C)

Dedicated to Yuri Grigor'evich Reshetnyak on his sixtieth birthday     

The subgroups of the group gl(2,k) that contain a nonsplit maximal torus

In the group GL(2,k), the lattice of the intermediate subgroups that contain the maximal nonsplit torus is studied for a field k of characteristic different from 2. In a number of cases, when formulating the results some additional restrictions are imposed. Bibliography: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 136–146. Translated by A. I. Skopin.     

One-parameter subgroups of the generalized Poincaré group p(2, n) and their invariants

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1169–1172, September, 1989.     

The reduced C1-algebra of the p-adic group GL(n)

The reduced C¹-algebra of the p-adic group GL(n) is Morita equivalent to an abelian C¹-algebra. The structure of this abelian C¹-algebra is described in terms of unramified unitary characters of Levi subgroups. The K-groups K₀ and K₁ are both free abelian of infinite rank. Generators are essentially parametrized by two items of Langlands data.