A free group acting without fixed points on the rational unit sphere
A Note on the Discontinuous Subgroups of the Orthogonal Group.
A splitting theorem for linear polycyclic groups.
A transvection decomposition in GL(n,2)
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
Absolute irreducibility for finitary linear groups
Distal affine transformation groups.
Finitary linear images of finitary linear groups.
Free groups acting without fixed points on rational spheres
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
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.
L’azione del gruppo simplettico associata ad un’estensione quadratica di campi
Linear groups with the maximal condition on subgroups of infinite central dimension.
Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension .
Matrix coefficients, counting and primes for orbits of geometrically finite groups
Let and for and when for , we obtain an effective archimedean counting result for a discrete orbit of in a homogeneous space where is the trivial group, a symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family of compact subsets, there exists such that for an explicit measure on which depends on . We also apply the affine sieve and describe the distribution of almost primes on orbits of in arithmetic settings....
Non-free two-generator subgroups of SL2(Q).
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| < 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.
On minimal Artinian modules and minimal Artinian linear groups.
On some infinite dimensional linear groups
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 linear groups factorized by mutually permutable subgroups
The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic...
Periodic subgroups of projective linear groups in positive characteristic
We classify the maximal irreducible periodic subgroups of PGL(q, ), where is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, ) containing the centre ×1q of GL(q, ), such that G/ ×1q is a maximal periodic subgroup of PGL(q, ), and if H is another group of this kind then H is GL(q, )-conjugate to a group in the list. We give criteria for determining...