November 2008. 24 x 17 cm. XX, 512 pages.
Hardcover ISBN 978-3-11-020418-6
Series: de Gruyter Expositions in Mathematics 46
Languages: English
Type of Publication: Monograph
This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular p-groups and regularity criteria, (c) p-groups of maximal class and their numerous characterizations, (d) characters of p-groups, (e) p-groups with large Schur multiplier and commutator subgroups, (f) (p?1)-admissible Hall chains in normal subgroups, (g) powerful p-groups, (h) automorphisms of p-groups, (i) p-groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index.
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.
November 2008. 24 x 17 cm. XV, 596 pages.
Hardcover. ISBN 978-3-11-020419-3
Series: de Gruyter Expositions in Mathematics 47
Languages: English
Type of Publication: Monograph
This is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n > 2, (f) two new proofs of Blackburn's theorem on minimal nonmetacyclic groups, (g) classification of p-groups all of whose subgroups of index p2 are abelian, (h) classification of 2-groups all of whose minimal nonabelian subgroups have order 8, (i) p-groups with cyclic subgroups of index p2 are classified.
This volume contains hundreds of original exercises (with all difficult exercises being solved) and an extended list of about 700 open problems. The book is based on Volume 1, and it is suitable for researchers and graduate students of mathematics with a modest background on algebra.
November 2008. 24 x 17 cm. XI, 527 pages.
Hardcover. ISBN 978-3-11-020536-7
Series: de Gruyter Expositions in Mathematics 45
Languages: English
Type of Publication: Monograph
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references.
From the contents: Field extensions ? Algebraic numbers ? Algebraic geometry ? Height functions ? The abc-conjecture ? Roth's theorem ? Subspace theorems ? Vojta's conjectures ? L-functions
November 2008. 24 x 17 cm. IX, 497 pages. 1 frontispiece.
Hardcover. ISBN 978-3-11-019437-1
Languages: English
Type of Publication: Collection
This is a memorial volume dedicated to A. L. S. Corner, previously Professor in Oxford, who published important results on algebra, especially on the connections of modules with endomorphism algebras. The volume contains refereed contributions which are related to the work of Corner. It contains also an unpublished extended paper of Corner himself.
A memorial volume with important contributions related to algebra.