Groups of Order P? Which Contain Cyclic Subgroups of Order P??? (Classic Reprint) - Hardcover

Lewis Irving Neikirk

9780428747435: Groups of Order P? Which Contain Cyclic Subgroups of Order P??? (Classic Reprint)

Hardcover

ISBN 10: 0428747434 ISBN 13: 9780428747435

Publisher: Forgotten Books, 2018

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Explore the structure of groups of order p^n and how cyclic subgroups shape their form.

This concise monograph explains how certain groups of order p^n can be identified by the presence of cyclic subgroups of specific orders, using clear, abstract methods that stay focused on the math itself.

This work presents a systematic approach to classifying these groups when p is an odd prime. It details how the groups are generated, how their defining relations are derived, and how the three main classes align with distinct partitions. Readers will see how the author translates complex group properties into explicit generational equations and how these lead to a complete, though focused, tabulation for groups of order p^n that contain cyclic subgroups of order p^n and none of higher order.

Learn the three-class framework and how partitions guide the classification of groups.
See how generators and relations are developed to describe each group explicitly.
Discover how transformations and congruences help identify when two descriptions define the same group.
Understand the methods used to extend results to broader cases while keeping the focus on p-groups with cyclic subgroups of order p^k.

Ideal for readers of advanced algebra and students seeking a rigorous, self-contained treatment of finite p-groups and their cyclic subgroups.

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