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On Groups of Order p α q β

1904
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Proceedings of the London Mathematical Society
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IT may be convenient to the reader to summarize the results hitherto obtained with regard to groups of order p a q^ other than those relating to particular values of p, q, a, and (3. If m is the index to which p belongs, mod. q, the first result arrived at was that, if a ^ m, the group is soluble.* In my book on the Theory of Groups (1897) I extended this result, showing that, if a < 2m, the group is soluble. In the same place I proved that, if the sub-groups of orders p a and q? are both

doi:10.1112/plms/s2-1.1.388
fatcat:l7v75lkn2fce3fy3mtj3fjl54m