Groups of Prime Power Order

Transcription

1 de Gruyter Expositions in Mathematics 56 Groups of Prime Power Order Volume 3 Bearbeitet von Yakov Berkovich, Zvonimir Janko 1. Auflage Buch. XXV, 639 S. Hardcover ISBN Format (B x L): 17 x 24 cm Gewicht: 1249 g Weitere Fachgebiete > Mathematik > Algebra schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents List of definitions and notations Preface ix xv Prerequisites from Volumes 1 and xvii Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent Nonabelian 2-groups of exponent 2 e which have no minimal nonabelian subgroups of exponent 2 e Groups with at most two conjugate classes of nonnormal subgroups p-groups in which some subgroups are generated by elements of order p Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M 2 nc1, n 3 fixed groups with sectional rank at most groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian p-groups G with p>2and d.g/ D 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian p-groups G with p>2and d.g/ > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian Some results of Jonah and Konvisser Degrees of irreducible characters of p-groups associated with finite algebras On some special p-groups On maximal subgroups of two-generator 2-groups

3 vi Groups of prime power order 107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups p-groups with few conjugate classes of minimal nonabelian subgroups On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p Equilibrated p-groups Characterization of abelian and minimal nonabelian groups Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order The class of 2-groups in 70 is not bounded Further counting theorems Finite p-groups all of whose maximal subgroups except one are extraspecial Groups covered by few proper subgroups groups all of whose nonnormal subgroups are either cyclic or of maximal class Review of characterizations of p-groups with various minimal nonabelian subgroups Review of characterizations of p-groups of maximal class Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection p-groups of breadth p-groups all of whose subgroups have normalizers of index at most p Subgroups of finite groups generated by all elements in two shortest conjugacy classes The number of subgroups of given order in a metacyclic p-group p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant The existence of p-groups G 1 <Gsuch that Aut.G 1 / Š Aut.G/ On 2-groups containing a maximal elementary abelian subgroup of order The commutator subgroup of p-groups with the subgroup breadth

4 Contents vii 129 On two-generator 2-groups with exactly one maximal subgroup which is not two-generator Soft subgroups of p-groups p-groups with a 2-uniserial subgroup of order p On centralizers of elements in p-groups Class and breadth of a p-group On p-groups with maximal elementary abelian subgroup of order p Finite p-groups generated by certain minimal nonabelian subgroups p-groups in which certain proper nonabelian subgroups are two-generator p-groups all of whose proper subgroups have its derived subgroup of order at most p p-groups all of whose nonnormal subgroups have the smallest possible normalizer p-groups with a noncyclic commutator group all of whose proper subgroups have a cyclic commutator group Power automorphisms and the norm of a p-group Nonabelian p-groups having exactly one maximal subgroup with a noncyclic center Nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm p-groups with small normal closures of all cyclic subgroups A.27 Wreathed 2-groups A.28 Nilpotent subgroups A.29 Intersections of subgroups A.30 Thompson s lemmas A.31 Nilpotent p 0 -subgroups of class 2 in GL.n; p/ A.32 On abelian subgroups of given exponent and small index

5 viii Groups of prime power order A.33 On Hadamard 2-groups A.34 Isaacs Passman s theorem on character degrees A.35 Groups of Frattini class A.36 Hurwitz theorem on the composition of quadratic forms A.37 On generalized Dedekindian groups A.38 Some results of Blackburn and Macdonald A.39 Some consequences of Frobenius normal p-complement theorem A.40 Varia A.41 Nonabelian 2-groups all of whose minimal nonabelian subgroups have cyclic centralizers A.42 On lattice isomorphisms of p-groups of maximal class A.43 Alternate proofs of two classical theorems on solvable groups and some related results A.44 Some of Freiman s results on finite subsets of groups with small doubling 527 Research problems and themes III Author index Subject index