Burnside Groups

John Joseph Tobin (1954), "On groups with exponent 4 " (PhD thesis, University of Manchester). Seán Tobin (1960), "Simple bounds for Burnside p-groups", Proc. Amer. Math. Soe. 11, 704–706. MR23#A202; Zbl.96, lö; RZ [1962], 8All!9.

Author: J. L. Mennicke

Publisher: Springer

ISBN: 9783540381204

Category: Mathematics

Page: 278

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Neutrosophic Extended Triplet Group Action and Burnside s Lemma

+905363214006 Abstract: The aim of this article is mainly to discuss the neutrosophic extended triplet (NET) group actions and Burnside's lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action.

Author: Moges Mekonnen Shalla

Publisher: Infinite Study

ISBN:

Category: Mathematics

Page: 26

View: 556

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The aim of this article is mainly to discuss the neutrosophic extended triplet (NET) group actions and Burnside’s lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action. Then, we give and proof the Orbit stabilizer formula for NET group by utilizing the notion of NET set theory. Moreover, some results related to NET group action, and Burnside’s lemma are obtained.

Groups Rings Lie and Hopf Algebras

Although the groups B(m,n) have plenty of free Burnside subgroups, the variety B, is not Schreier for n > 2, that is, a subgroup of a free Burnside group is not necessarily n was free in Bn. This follows from Neumann – Wiegold's theorem ...

Author: Y. Bahturin

Publisher: Springer Science & Business Media

ISBN: 9781461302353

Category: Mathematics

Page: 241

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The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Biset Functors for Finite Groups

Let G be a arbitrary group. At this level of generality, there are several possibilities for the definition of the Burnside group of G: it is always defined as the Grothendieck group of some category of G-sets, but this category depends ...

Author: serge Bouc

Publisher: Springer

ISBN: 9783642112973

Category: Mathematics

Page: 306

View: 132

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This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.

Infinite Groups 1994

Our proof uses the solution to the restricted Burnside problem given by E. ZelInanoV. We shall recall next some general ideas about Burnside problems: General Burnside Problem. Is a periodic group locally finite?

Author: Francesco Giovanni

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110810387

Category: Mathematics

Page: 344

View: 620

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The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Yakov Berkovich Zvonimir Janko Groups of Prime Power Order

order 212 and exponent 4 and so G is the Burnside group. The group G has exactly k(G) : 88 conjugate classes. The automorphism group of G is of order 221 - 3. Proof. This theorem (apart from the last statement) is proved by using a ...

Author: Yakov Berkovich

Publisher: Walter de Gruyter

ISBN: 9783110208238

Category: Mathematics

Page: 611

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This is the second of three volumes on finite p-group theory, written by two prominent authors in the area.

Topics in Groups and Geometry

In this chapter we discuss some instances of the Burnside Problem. There are three versions of this problem, the first one being the General Burnside Problem: Is it true that if a group G is finitely generated and torsion, ...

Author: Tullio Ceccherini-Silberstein

Publisher: Springer Nature

ISBN: 9783030881092

Category: Electronic books

Page: 464

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This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov's pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov's theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

Groups and Characters

Chapter 17 The Burnside Counting Theorem In this chapter we'll apply some group theory to counting problems . In particular , a pure group - theoretic result of W. F. Burnside ( Theory of Groups of Finite Order , 2nd ed .

Author: Victor E Hill

Publisher: CRC Press

ISBN: 1584880384

Category: Mathematics

Page: 239

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Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters. Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5. The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory. Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.

Combinatorial and Geometric Group Theory

seG64] [GS83] InC89) [rG80) [I94 [I00 [IO96) [IO97) [L96] [NA68] (O82] [O89) E.S. Golod, On nil-algebras and residually finite p-groups, Math. USSR Izvestiya 28(1964), 273–276. N. Gupta and S. Sidki, On the Burnside problem for periodic ...

Author: Sean Cleary

Publisher: American Mathematical Soc.

ISBN: 9780821828229

Category: Mathematics

Page: 275

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This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

A First Course in Noncommutative Rings

( 9.2 ) Bounded Burnside Problem ( BBP ) . Let G be a finitely generated group of bounded exponent . Is G necessarily finite ? One of the main goals of this section is to study these two problems for linear groups .

Author: Tsit-Yuen Lam

Publisher: Springer Science & Business Media

ISBN: 0387951830

Category: Mathematics

Page: 385

View: 711

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Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.