Representation theoretic existence proof for Fischer group Fi_{23}

Details Representation theoretic existence proof for Fischer group Fi_{23} Representation theoretic existence proof for Fischer group Fi_{23}

2009-04-03

arxiv.org/abs/0904.0639v1

Mathematics

Group Theory

102 pages; undergraduate senior thesis in Cornell (May 2008)

Scientific paper

In the first section of this senior thesis the author provides some new efficient algorithms for calculating with finite permutation groups. They cannot be found in the computer algebra system MAGMA, but they can be implemented there. For any finite group G with a given set of generators, the algorithms calculate generators of a fixed subgroup of G as short words in terms of original generators. Another new algorithm provides such a short word for a given element of G. In the later sections, the author gives a self-contained existence proof for Fischer's sporadic simple group Fi_{23} using G. Michler's Algorithm [11] constructing finite simple groups from irreducible subgroups of GL_n(2). This sporadic group was originally discovered by B. Fischer in [6] by investigating 3-transposition groups, see also [5]. This thesis gives a representation theoretic and algorithmic existence proof for his group. The author constructs the three non-isomorphic extenstions E_i by the two 11-dimensional non-isomorphic simple modules of the Mathieu group M_{23} over F=GF(2). In two cases Michler's Algorithm fails. In the third case the author constructs the centralizer H=C_G(z) of a 2-central involution z of E_i in any target simple group G. This allows the author to construct G inside GL_{782}(17). Its four generating matrices, character table and representatives for conjugacy classes are computed. It follows that G and Fi_{23} have the same character table.

Affiliated with

Also associated with

No associations

Rating

Representation theoretic existence proof for Fischer group Fi_{23} does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representation theoretic existence proof for Fischer group Fi_{23}, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representation theoretic existence proof for Fischer group Fi_{23} will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151382