Groups of Prime Power Order Volume 3 1st Edition by Yakov Berkovich, Zvonimir Janko ISBN 3110254484 9783110254488

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Product details:

ISBN 10: 3110254484

ISBN 13: 9783110254488

Author:  Yakov Berkovich, Zvonimir Janko 

Groups of Prime Power Order Volume 3 1st Edition: 

This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume:

• impact of minimal nonabelian subgroups on the structure of p-groups,
• classification of groups all of whose nonnormal subgroups have the same order,
• degrees of irreducible characters of p-groups associated with finite algebras,
• groups covered by few proper subgroups,
• p-groups of element breadth 2 and subgroup breadth 1,
• exact number of subgroups of given order in a metacyclic p-group,
• soft subgroups,
• p-groups with a maximal elementary abelian subgroup of order p²,
• p-groups generated by certain minimal nonabelian subgroups,
• p-groups in which certain nonabelian subgroups are 2-generator.

The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.

 

Groups of Prime Power Order Volume 3 1st Edition Table of contents:

Prerequisites from Volumes 1 and 2

§93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent

§94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have expone

§95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e

§96 Groups with at most two conjugate classes of nonnormal subgroups

§97 p-groups in which some subgroups are generated by elements of order p

§98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n∈ 3 f

§99 2-groups with sectional rank at most 4

§100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian

§101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelia

§102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelia

§103 Some results of Jonah and Konvisser

§104 Degrees of irreducible characters of p-groups associated with finite algebras

§105 On some special p-groups

§106 On maximal subgroups of two-generator 2-groups

§107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups

§108 p-groups with few conjugate classes of minimal nonabelian subgroups

§109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p

§110 Equilibrated p-groups

§111 Characterization of abelian and minimal nonabelian groups

§112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order

§113 The class of 2-groups in §70 is not bounded

§114 Further counting theorems

§115 Finite p-groups all of whose maximal subgroups except one are extraspecial

§116 Groups covered by few proper subgroups

§117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class

§118 Review of characterizations of p-groups with various minimal nonabelian subgroups

§119 Review of characterizations of p-groups of maximal class

§120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic inters

§121 p-groups of breadth 2

§122 p-groups all of whose subgroups have normalizers of index at most p

§123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes

§124 The number of subgroups of given order in a metacyclic p-group

§125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant

§126 The existence of p-groups G1 < G such that Aut(G1) ≅ Aut(G)

§127 On 2-groups containing a maximal elementary abelian subgroup of order 4

§128 The commutator subgroup of p-groups with the subgroup breadth 1

§129 On two-generator 2-groups with exactly one maximal subgroup which is not two-generator

§130 Soft subgroups of p-groups

§131 p-groups with a 2-uniserial subgroup of order p

§132 On centralizers of elements in p-groups

§133 Class and breadth of a p-group

§134 On p-groups with maximal elementary abelian subgroup of order p2

§135 Finite p-groups generated by certain minimal nonabelian subgroups

§136 p-groups in which certain proper nonabelian subgroups are two-generator

§137 p-groups all of whose proper subgroups have its derived subgroup of order at most p

§138 p-groups all of whose nonnormal subgroups have the smallest possible normalizer

§139 p-groups with a noncyclic commutator group all of whose proper subgroups have a cyclic commuta

§140 Power automorphisms and the norm of a p-group

§141 Nonabelian p-groups having exactly one maximal subgroup with a noncyclic center

§142 Nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal

§143 Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm

§144 p-groups with small normal closures of all cyclic subgroups

 

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