National Institute of Technology Rourkela

राष्ट्रीय प्रौद्योगिकी संस्थान राउरकेला

ଜାତୀୟ ପ୍ରଯୁକ୍ତି ପ୍ରତିଷ୍ଠାନ ରାଉରକେଲା

An Institute of National Importance

Syllabus

Course Details

Subject {L-T-P / C} : MA6645 : Group Theory and its Application { 3-1-0 / 4}

Subject Nature : Theory

Coordinator : Dr. Bikramaditya Sahu

Syllabus

General and special linear groups, bilinear forms, Symplectic groups, symmetric forms, quadratic forms, Orthogonal geometry, orthogonal groups, Clifford algebras, Hermitian forms, Unitary spaces, Unitary groups.

Course Objectives

  • To give an introduction to different types of finite classical groups
  • To study the simplicity of Sympletic, Orthogonal and Unitary groups
  • To study some applications in Finite Geometry

Course Outcomes

This course will help students to learn certain matrix groups over finite fields and their simplicity. This will help to do research in finite geometry, representation theory and related areas.

Essential Reading

  • L. C. Grove, Classical Groups and Geometric Algebra, Graduate Studies in Mathematics 39, American Mathematical Society, 2002
  • E. Artin, Geometric Algebra, John Wiley & sons, 1988

Supplementary Reading

  • L. M. Batten, Combinatorics of Finite Geometries, Cambridge University Press, 1997
  • G. E. Moorhouse, Incidence Geometry, 2007, available online from http://www.uwyo.edu/moorhouse/handouts/incidence geometry.pdf