Computing in the Monster

Computing in the Monster

We give a survey of computational methods and results concerning the Monster sporadic simple group. There are now three computer constructions of the Monster which are proving effective in answering real questions about this group. The first construction over the field of two elements is the fastest for calculations, and has been used to show the group is a Hurwitz group. The second constructio...

The “monster” Study

The diagnosogenic (semantogenic) theory for the onset of stuttering was initially proposed by Wendell Johnson in the early 1940s. It suggested that calling attention to a child’s normal hesitations (repetitions) could precipitate stuttering (Bloodstein, 1987). Some of the evidence that Johnson used to support this theory (e.g., certain tribes of American Indians, in which there appeared to be n...

Product Replacement in the Monster

;its minimal faithful permutation and matrix representation degrees are respectively 97 239 461 142 009 186 000 and 196 882. This makes it far harder to work with than the 25 smaller sporadics. In Section 3, we describe techniques which allow limited computation in the Monster. In Section 4, we describe our experiments to assess the effectiveness of combining these techniques with a suitable ve...

New computations in the Monster

We survey recent computational results concerning the Monster sporadic simple group. The main results are: progress towards a complete classification of the maximal subgroups, including showing that L2(27) is not a subgroup; showing that the 196882-dimensional module over GF (2) supports a quadratic form; a complete set of explicit conjugacy class representatives; small representations of most ...

Taming the Cookie Monster