Read e-book online Atlas of finite groups: maximal subgroups and ordinary PDF

By John Horton Conway

ISBN-10: 0198531990

ISBN-13: 9780198531999

This atlas covers teams from the households of the category of finite easy teams. lately up to date incorporating corrections

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Additional info for Atlas of finite groups: maximal subgroups and ordinary characters for simple groups

Sample text

G (or M. G. A) with a large multiplier, we have always arranged that for any given g, the displayed pre-images of g in all the cyclic extensions m. G are all images of a 'universal' pre-image of g in M. G. 'Dually', we have arranged whenever possible that the prolongations of a given character to all the cyclic extensions G. a are restrictions of a 'universal' character defined on G. A. There are still some choices that are more virtuous than others. For example in a group of structure 2 2 • G .

An extremely valuable test which we recommend when the above simple rules of thumb have failed is to compute the skew squares of one or more characters X, and check their inner products with selected irreducibles. One should also check the consistency of restriction maps from groups to subgroups whose tables are also known. Of course it can be a good idea to check a doubtful point against another published table, which might well be the one from which ours was originally derived. A disagreement probably means that we believed we had found and corrected an error in the source table, but of course we could be wrong, or could have inadvertently introduced some error ourselves.

Format Tables with columns of randomly varying widths have a 'ragged' appearance which is very wearying to the reader. In our tables the only permitted widths are 4, 6, 8, ... spaces. We have taken great pains, particularly with our irrationality conventions, to ensure that most columns will fit into the standard width of 4 spaces, so that large tracts of table have a regular layout. The even-width requirement entails that a wider column is seen to be wider----<:olumns whose widths are nearly but not quite equal producea slightly disorienting effect.

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Atlas of finite groups: maximal subgroups and ordinary characters for simple groups by John Horton Conway

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