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### A free group acting without fixed points on the rational unit sphere

Fundamenta Mathematicae

### A Note on the Discontinuous Subgroups of the Orthogonal Group.

Mathematische Zeitschrift

### A splitting theorem for linear polycyclic groups.

The New York Journal of Mathematics [electronic only]

### A transvection decomposition in GL(n,2)

Colloquium Mathematicae

An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.

### A unipotent group associated with certain linear groups

Colloquium Mathematicae

### Absolute irreducibility for finitary linear groups

Rendiconti del Seminario Matematico della Università di Padova

### Distal affine transformation groups.

Journal für die reine und angewandte Mathematik

### Finitary linear images of finitary linear groups.

Mathematica Pannonica

### Free groups acting without fixed points on rational spheres

Acta Arithmetica

For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.

### Infinite dimensional linear groups with many G - invariant subspaces

Open Mathematics

Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.

Bollettino dell'Unione Matematica Italiana

### Linear groups with the maximal condition on subgroups of infinite central dimension.

Publicacions Matemàtiques

### Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension .

Publicacions Matemàtiques

### Matrix coefficients, counting and primes for orbits of geometrically finite groups

Journal of the European Mathematical Society

Let $G:=\mathrm{SO}{\left(n,1\right)}^{\circ }$ and $\Gamma \left(n-1\right)/2$ for $n=2,3$ and when $\delta >n-2$ for $n\ge 4$, we obtain an effective archimedean counting result for a discrete orbit of $\Gamma$ in a homogeneous space $H\setminus G$ where $H$ is the trivial group, a symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family $\left\{{ℬ}_{T}\subset H\setminus G\right\}$ of compact subsets, there exists $\eta >0$ such that $#\left[e\right]\Gamma \cap {ℬ}_{T}=ℳ\left({ℬ}_{T}\right)+O\left(ℳ{\left({ℬ}_{T}\right)}^{1-\eta }\right)$ for an explicit measure $ℳ$ on $H\setminus G$ which depends on $\Gamma$. We also apply the affine sieve and describe the distribution of almost primes on orbits of $\Gamma$ in arithmetic settings....

### Non-free two-generator subgroups of SL2(Q).

Publicacions Matemàtiques

The question of whether two parabolic elements A, B of SL2(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| &lt; 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL2(C) will not be free.

### On L-Groups.

Mathematische Annalen

### On minimal Artinian modules and minimal Artinian linear groups.

International Journal of Mathematics and Mathematical Sciences

### On some infinite dimensional linear groups

Open Mathematics

Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.

### Periodic subgroups of projective linear groups in positive characteristic

Open Mathematics

We classify the maximal irreducible periodic subgroups of PGL(q, $𝔽$ ), where $𝔽$ is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and $𝔽$ × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, $𝔽$ ) containing the centre $𝔽$ ×1q of GL(q, $𝔽$ ), such that G/$𝔽$ ×1q is a maximal periodic subgroup of PGL(q, $𝔽$ ), and if H is another group of this kind then H is GL(q, $𝔽$ )-conjugate to a group in the list. We give criteria for determining...

### Periodic-by-nilpotent linear groups

Rendiconti del Seminario Matematico della Università di Padova

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