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Excerpt from Groups of Order Pm Which Contain Cyclic Subgroups of Order Pm-3
Although in the present state of the theory, the actual tabulation of all groups of order p' is impracticable, it is of importance to carry the tabu lation as far as may be possible. In this paper all groups of order p' (1) being an odd prime) which contain cyclic subgroups of order p'-3 and none of higher order are determined. The method of treatment used is entirely abstract in character and, in virtue of its nature, it is possible in each case to give explicitly the generational equations of these groups. They are divided into three classes, and it will be shown that these classes correspond to the three partitions (m 3 (m 3 2, 1) and (m - 3, 1, 1, of m.
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