Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order. Volume 1

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<p>This is the first of three volumes of a comprehensive and elementary treatment of finite <em>p</em>-group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular <em>p</em>-groups and regularity criteria, (c)<em> p</em>-groups of maximal class and their numerous characterizations, (d) characters of <em>p</em>-groups, (e) <em>p</em>-groups with large Schur multiplier and commutator subgroups, (f) (<em>p</em>‒1)-admissible Hall chains in normal subgroups, (g) powerful <em>p</em>-groups, (h) automorphisms of <em>p</em>-groups, (i) <em>p</em>-groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index.</p> <p>The book is suitable for researchers and graduate students of mathematics with a modest background on algebra. It also contains hundreds of original exercises (with difficult exercises being solved) and a comprehensive list of about 700 open problems.</p>