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Excerpt from Groups of Order Pᵐ Which Contain Cyclic Subgroups of Order Pᵐ⁻ᶟ
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 gym - 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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Groups of Order Páµ Which Contain Cyclic Subgroups of Order Páµâ»á
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Paperback. Condition: New. Print on Demand. This book offers an in-depth examination of finite groups. It builds on Burnside's theory of finite groups and extends the study of cyclic subgroups of prime power index. The focus is on a particular type of group with cyclic subgroups of order p , where p is a prime number, and a detailed classification is presented. The author also discusses the relationship between these groups and other types of finite groups, providing insights into their structure and properties. The book's comprehensive analysis and classification of these groups are valuable contributions to the field of group theory, offering a deeper understanding of their characteristics and significance within the broader context of finite group theory. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332944668_0
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