Alperin–Brauer–Gorenstein theorem

From formulasearchengine
Jump to navigation Jump to search

In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathed[1] Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective special unitary groups over a finite fields of odd order, depending on a certain congruence, or to the Mathieu group . Template:Harvtxt proved this in the course of 261 pages. The subdivision by 2-fusion is sketched there, given as an exercise in Template:Harvtxt, and presented in some detail in Template:Harvtxt.

Notes

  1. A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a direct product of two cyclic groups of the same order, that is, if it is the wreath product of a cyclic 2-group with the symmetric group on 2 points.

References

  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}

  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}

  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}


Template:Abstract-algebra-stub