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Izv. Akad. Nauk SSSR Ser. Mat. Tom 38 (1974), No. 4 Math. USSR Izvestija Vol. 8 (1974), No. 4 IMPOTENT GROUP SCHEMES OVER INTEGRAL RINGS UDC 519.4 B. Ju. VEISFEILER AND I. V. DOLGACEV Abstract. In.

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The radical of an algebraic group is contained in every Borel subgroup, but the Borel subgroups may be strictly bigger. There is a corresponding notion for groups without algebraic structure, which we also call the radical (or solvable radical) -- this is simply the largest solvable normal subgroup.

The unipotent radical of an algebraic group G is the set of unipotent elements in the radical of G. It is a connected unipotent normal subgroup of G, and contains all other such subgroups. A group is called reductive if its unipotent radical is trivial. If G is reductive then its radical is a torus.

The unipotent radical Ru(G) of a linear algebraic group G is its maximal connected unipotent normal subgroup. A group is reductive if its unipotent radical over the algebraic closure, Ru(G¯k), is trivial, and semisimple if R(G) = 1.

Let q=pr. The eigenvalues of a unipotent matrix are all 1 and so we may conjugate it into Jordan canonical form without extending the field. This yields a unipotent upper triangular matrix with entries in Z/pZ. Thus the answer is independent of r.

The regular unipotent elements of G form a single conjugacy class and are dense in the unipotent variety, with a typical centralizer CG(u)=Z(G)CU(u) (which equals CU(u) when G is simple in the group-theoretic sense).

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Keywords relevant to UNIPOTENT GROUP SCHEMES OVER INTEGRAL RINGS

  • Lemma
  • p-polynomial
  • Commutative
  • Isomorphism
  • isomorphic
  • xj
  • jU
  • homomorphism
  • DOLGACEV
  • VEISFEILER
  • Topology
  • S-Group
  • xv
  • SGAD
  • YJ
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© Copyright 1997-2025
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Form Packages
Adoption
Bankruptcy
Contractors
Divorce
Home Sales
Employment
Identity Theft
Incorporation
Landlord Tenant
Living Trust
Name Change
Personal Planning
Small Business
Wills & Estates
Packages A-Z
Form Categories
Affidavits
Bankruptcy
Bill of Sale
Corporate - LLC
Divorce
Employment
Identity Theft
Internet Technology
Landlord Tenant
Living Wills
Name Change
Power of Attorney
Real Estate
Small Estates
Wills
All Forms
Forms A-Z
Form Library
Customer Service
Terms of Service
DMCA Policy
About Us
Blog
Affiliates
Contact Us
Privacy Notice
Delete My Account
Site Map
All Forms
Search all Forms
Industries
Forms in Spanish
Localized Forms
Legal Guides
Real Estate Handbook
All Guides
Prepared for You
Notarize
Incorporation services
Our Customers
For Consumers
For Small Business
For Attorneys
Our Sites
US Legal Forms
USLegal
FormsPass
pdfFiller
signNow
airSlate workflows
DocHub
Instapage
Social Media
Call us now toll free:
1-877-389-0141
As seen in:
  • USA Today logo picture
  • CBC News logo picture
  • LA Times logo picture
  • The Washington Post logo picture
  • AP logo picture
  • Forbes logo picture
© Copyright 1997-2025
airSlate Legal Forms, Inc.
3720 Flowood Dr, Flowood, Mississippi 39232