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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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  1. Begin by clicking the ‘Get Form’ button to access the UNIPOTENT GROUP SCHEMES OVER INTEGRAL RINGS form and open it in the online editor.
  2. In the first section, provide the name and details of the group scheme you are referring to. Ensure that you accurately describe the integral ring associated with your group scheme.
  3. Next, complete the fields that request information on the unipotent algebraic properties. Follow the guidelines provided to specifically outline characteristics that pertain to your group scheme, including the necessary definitions and properties.
  4. In the subsequent section, detail the geometric aspects of the group scheme. Include any cohomological results or relationships that pertain specifically to the family of unipotent groups in question.
  5. Proceed to input any examples or counterexamples that you may have in relation to your research, ensuring all conditions are met accurately as stipulated in the form instructions.
  6. After completing all the required sections, review your inputs for accuracy. Make adjustments as needed to comply with the form requirements.
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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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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
Privacy Notice
Legal Hub
Content Takedown Policy
Bug Bounty Program
About Us
Blog
Affiliates
Contact Us
Delete My Account
Site Map
Industries
Forms in Spanish
Localized Forms
State-specific Forms
Forms Kit
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 WorkFlow
DocHub
Instapage
Social Media
Call us now toll free:
+1 833 426 79 33
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