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Tuesday, August 4, 2020 | History

2 edition of On the structure of the group ring of a p-group over a modular field found in the catalog.

On the structure of the group ring of a p-group over a modular field

Stephen Arthur Jennings

# On the structure of the group ring of a p-group over a modular field

## by Stephen Arthur Jennings

Written in English

Edition Notes

Thesis (Ph.D.)--University of Toronto, 1939.

 ID Numbers Statement Stephen Arthur Jennings. Open Library OL14849226M

Algebraic Structures Graphic Organizer: Earn up to +5% toward your final grade by creating a graphic representation of how each of the following algebraic structures are related: Semigroup, Monoid, Group, Ring, Integral Domain, Principle Ideal Domain, Unique Factorization Domain, Field. Construction of free subgroups in the group of units of modular group algebras (with J. Z. Goncalves) - Let K[G] denote the group algebra of a p'-group G over a field K of characteristic p > 0 and let U = U(K[G]) be its group of units. If K[G] contains a bicyclic unit and if K is not algebraic over its prime subfield, then we prove that the.

Conjugacy Classes. The conjugacy classes of elements of a group G are found using a lifting algorithm which first finds the classes of the trivial Fitting quotient of G (algorithm of D. Holt) and then lifts these classes through the layers of an elementary abelian series for example, all classes in the group 2 (SL 2 (4) ≀ S 3) of degree and order 5,,, are. The Klein four-group is thus also the group generated by the symmetric difference as the binary operation on the subsets of a powerset of a set with two elements, i.e. over a field of sets with four elements, e.g. {∅, {}, {}, {,}}; the empty set is the group's identity element in this case.

Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat. This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. which says that a finite subgroup of the p-adic integral group ring of a finite p-group is conjugate to a subgroup of the finite group.

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### On the structure of the group ring of a p-group over a modular field by Stephen Arthur Jennings Download PDF EPUB FB2

THE STRUCTURE OF THE GROUP RING OF A ^-GROUP OVER A MODULAR FIELD by S. JENNINGS This paper deals with the group ring of a group of prime power order over the prime field GF(p), where p is the prime dividing the order of the group.

It is well known that in the case of the group ring of a group over a field. the modular group-ring of a finite p-group the quaternion, dihedral and semidihedral groups; furthermore the groups P = (g,h/g2n = h2 = 1, gh = g1+2n_1) belong to the list.

In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of p n copies of g, and not fewer, is equal to the identity orders of different elements may be different powers of p.

S.A. Jennings, The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc. 50 (), – MathSciNet zbMATH Google ScholarAuthor: Shigeo Koshitani.

Again, it is easily seen that is an er, if is commutative, it follows that is an algebra over, and in this case it is frequently called the group algebra of over.

The map given by is a ring homomorphism; it is called the augmentation map of and plays a central role in the theory. In view of the intimate connection with representation theory, it is natural to ask to which.

This gives the circle group the structure of a one-parameter group, an instance of a Lie group. In fact, up to isomorphism, it is the unique 1 dimensional compact, connected Lie group. Moreover, every n {\displaystyle n} dimensional compact, connected, abelian Lie group is isomorphic to T n {\displaystyle \mathbb {T} ^{n}}.

ISOMORPHISMS OF r)-ADIC GROUP RINGS nilpotent modulo pA or p”A.) This gives c#P E p”End,R for all large m, and so+* +Oasm+ co. are now ready for the proof of Theorem 2. Abstract. This paper is devoted to the study of finite p-groups and their inverse limits, with special emphasis on recent developments and applications of Lie theory (in a broad sense, which includes Lie algebras and Lie groups).The main topics covered are: fixed point theorems, powerful groups and p-adic analytic groups, the Restricted Burnside Problem, the proof of the Coclass Conjectures Cited by: Abstract.

We make a systematic study of filtrations of a free group F defined as products of powers of the lower central series of some assumptions on the exponents, we characterize these filtrations in terms of the group algebra, the Magnus algebra of non-commutative power series, and linear representations by upper-triangular unipotent matrices.

Let J(KG) be the Jacobson radical of the group algebra KG of a finite p-solvable group G over a field K of characteristic p > 0, and let t(G) be the least positive integer t such that J(KG)t = : Shigeo Koshitani. To every nite p-group one can associate a Lie ring L(G), and if G=G0is elementary abelian then L(G) is actually a Lie algebra over the nite eld GF(p).

Proposition Let ˚be an automorphism of the nite p-group G. Then ˚induces an automorphism on L(G), and if ˚has order prime to p, then the induced automorphism has the same Size: KB. MR Jennings, S. (), "The structure of the group ring of a p-group over a modular field", Transactions of the American Mathematical Society Coclass ( words) [view diff] no match in snippet view article find links to article.

We follow Greenberg in our definition of the Selmer group Sel (F ∞, A) for f over F ∞, which carries the structure of a cofinitely generated discrete O-torsion Λ-module, where Λ = O [[Γ]] is the completed group ring of Γ with coefficients in O and A is a cofree O-module of corank 2 arising from a choice of G F-stable O-lattice in the p Cited by: 6.

A structure of MZP Group is based on our aim to be as close to our customers all over the world as possible, along with a requirement for maximum efficiency and flexibility in activities of our particular subsidiaries as well as the entire group. Balogh, T. JuhÃ¡sz, Derived lengths of symmetric and skew symmetric elements in group algebras, JP J.

Algebra Number Theory Appl. 12 (2) () â€“ [4] S.A. Jennings, The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc. 50 () â€“ [5] by: 3. Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and.

As a consequence we obtain a general structure theorem for Galois extensions with given p-group as Galois group and any prescribed commutative k-algebra R as invariant ring. This is a generalization of the Artin–Schreier–Witt theory of modular Galois field extensions of degree ps.

General linear group of a vector space. If V is a vector space over the field F, the general linear group of V, written GL(V) or Aut(V), is the group of all automorphisms of V, i.e.

the set of all bijective linear transformations V → V, together with functional composition as group V has finite dimension n, then GL(V) and GL(n, F) are isomorphic. Let $\Gamma$ be a discrete group, and let $\Bbb{C}[\Gamma]$ be the associated complex group ring.

If $\sum_{g \in \Gamma} a_g g$ represents some element in the group ring, where all but finitely many. In this book we define the new notion of neutrosophic rings. The motivation for this study is two-fold.

Firstly, the classes of neutrosophic rings defined in this book are generalization of the two well-known classes of rings: group rings and semigroup rings. Semi idempotents in the group ring of a cyclic group over the field of rationals Author: Kandasamy Vasantha and Florentin Smarandache.

'In summary, this book provides a thorough introduction to the theory of the correspondence between modular representations of elementary abelian groups and vector bundles over projective space. In it the reader will find results from the literature, as well as new contributions to the by: 8.You can write a book review and share your experiences.

Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.• 9MAY From:y,USN/ To: Superintendant, ostgraduateSchool (TechnicalLibrary) Monterey,California Subj.