Presentations for $3$-dimensional special linear groups over integer rings
نویسندگان
چکیده
منابع مشابه
The Homology of Special Linear Groups over Polynomial Rings
We study the homology of SLn(F [t, t ]) by examining the action of the group on a suitable simplicial complex. The E–term of the resulting spectral sequence is computed and the differential, d, is calculated in some special cases to yield information about the low-dimensional homology groups of SLn(F [t, t ]). In particular, we show that if F is an infinite field, then H2(SLn(F [t, t ]), Z) = K...
متن کاملLow Dimensional Homology of Linear Groups over Hensel Local Rings
We prove that if R is a Hensel local ring with infinite residue field k, the natural map Hi(GLn(R),Z/p) → Hi(GLn(k), Z/p) is an isomorphism for i ≤ 3, p 6= char k. This implies rigidity for Hi(GLn), i ≤ 3, which in turn implies the Friedlander–Milnor conjecture in positive characteristic in degrees ≤ 3. A fundamental question in the homology of linear groups is that of rigidity: given a smooth ...
متن کاملFlag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
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This work presents block codes over Gaussian integer rings. Rings of Gaussian integers extend the number of possible QAM signal constellations over Gaussian integer fields. Many well-known code constructions can be used for codes over Gaussian integer rings, e.g., the Plotkin construction or product codes. These codes enable low complexity soft decoding in the complex domain.
متن کاملShort presentations for three-dimensional unitary groups
We give a presentation of length O ( log2 |G| ) for the groups G∼= PSU3(q). This result has applications in recent algorithms to compute the structure of permutation groups and matrix groups.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1079696-5