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Saturday, July 11, 2020 | History

3 edition of On the Loewy structure of projective modules for some semilinear groups found in the catalog.

On the Loewy structure of projective modules for some semilinear groups

Brian S. Pilz

On the Loewy structure of projective modules for some semilinear groups

by Brian S. Pilz

  • 274 Want to read
  • 13 Currently reading

Published .
Written in English

    Subjects:
  • Finite groups.,
  • Modular representations of groups.,
  • Projective modules (Algebra)

  • Edition Notes

    Statementby Brian S. Pilz.
    Classifications
    LC ClassificationsMicrofilm 95/4052 (Q)
    The Physical Object
    FormatMicroform
    Paginationiii, 81 leaves
    Number of Pages81
    ID Numbers
    Open LibraryOL961141M
    LC Control Number95953119

    Hahn, Isomorphisms of projective orthogonal groups and subgroups A corollary of 3. 2 is a non-projective analogue (). Series of examples of groups satisfying property P are listed in § 4. The groups of [9] (over infinite fields) and their projective groups are included in this theory. The AMS Bookstore is open, but rapid changes related to the spread of COVID may cause delays in delivery services for print products. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase.

    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.,,, Free ebooks since In fact, the dimensions of simple L-modules are bounded above, and there has been considerable interest in determining a least upper bound for some classes of Lie algebras, especially for simple Lie algebras of classical type [Ru1, VK, FP7]1 and Cartan type [Mil1, Mil2, Kry1] (cf. also [Pan, Kry2] and [Hum3, Problem4]).

    AMERICAN MATHEMATICAL SOCIETY Vol Number 4, October Representation theory of Artin algebras, by Maurice Auslander, Idun Reiten, and Serre O. Smal˝, Cambridge Stud. Adv. Math., vol. 36, Cambridge Univ. Press, , xiv+ pp., $, ISBN Here is the book you may have been waiting for for a long time, maybe for fteen. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. group-theory finite-groups normal-subgroups finitely-generated derived-subgroup. modified 48 mins ago Equivalent properties of integral domain f.g projective modules. commutative-algebra modules projective.


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On the Loewy structure of projective modules for some semilinear groups by Brian S. Pilz Download PDF EPUB FB2

The so-called Cartan integers are the multiplicities of the irreducible kG-modules within the corresponding projective, indecomposable kG-modules. In this paper, formulae for the Cartan integers for the semilinear groups ΣL(2, 2 n) are exhibited as quotients of sums of algebraic integers.

Additionally, the second Loewy layer of the projective, indecomposable modules are : B.S. Pilz. The so-called Cartan integers are the multiplicities of the irreducible kG-modules within the corresponding projective, indecomposable kG-modules. In this paper, formulae for the Cartan integers for the semilinear groups ΣL(2, 2n) are exhibited as quotients of sums of algebraic : B.S.

Pilz. Dissertation: On the Loewy Structure of Projective Modules for Some Semilinear Groups Mathematics Subject Classification: 20—Group theory and. On the Loewy length of modules of finite projective dimension Puthenpurakal, Tony J., Journal of Commutative Algebra, On the Structure of the Fundamental Series of Generalized Harish-Chandra Modules Penkov, Ivan and Zuckerman, Gregg, Asian Journal of Mathematics,   Landrock P.

() Some remarks on Loewy lengths of projective modules. In: Dlab V., Gabriel P. (eds) Representation Theory II.

Lecture Notes in Mathematics, vol Cited by: 1. AN UPPER BOUND FOR LOEWY LENGTHS OF PROJECTIVE MODULES IN P-SOLVABLE GROUPS WOLFGANG WILLEMS (Received October 8, ) 1.

Introduction. Let p be a prime, F a field of characteristic p and let G be a finite group. With every FG-module M there is attached a non-negative integer L(M) called the Loewy length of M.

If J(FG) denotes the Jacobson radical of FG 9File Size: KB. We determine all finite groups G such that the Loewy length (socle length) of the projective cover P(kG) of the trivial kG-module k G is four, where k is a field of characteristic P > 0 and kG is the group algebra of G over k, by using previous results and also the classification of finite simple : Shigeo Koshitani.

reducibles for the groups of Lie type. He also has chapters describing some related problems: decomposition numbers, Cartan invariants, extensions between simple mod ules, Loewy structure (i.e., description of the radical layers) of projective indecom posable modules, complexity and support varieties, and so on.

The book is very dense. It would be. We compute the Loewy structure of the indecomposable projective modules for the group algebra FG, where G is the alternating group on 10 letters and F is an algebraically closed field of.

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.

The general linear group. We introduce the projective geometry PG(V) associated to a finite dimensional vector space V and the general linear group GL(V), as well as the general semilinear group γL(V).

We describe the re- lations between these groups and their projective. Note that R M is a free module if and only if R M has shape m k. Recall that a module R M is projective (resp., injective) if R M is a direct summand of a free module (resp., a direct summand of every module containing R M).

In this section, we introduce the projective Hjelmslev geometries PHG(R k R)andgive some results on their basic. Among other topics, projective Schur index and projective representations of abelian groups are covered.

The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras.

We study the branching rules between K(Sp×Sp) and KS2p: that is we determine, in characteristic p for p odd, the Loewy structure of the principal block simple K(Sp×Sp)-modules induced to KS2p and the Loewy structure of the principal block simple KS2p-modules restricted to K(Sp×Sp).Cited by: 1.

The loewy structure of the projective indecomposable modules for the mathieu groups in characteristic 3. Communications in Algebra, Vol. 21, Issue. 5, p. Cited by: Particularly striking is the influence of algebraic geometry and cohomology theory in the modular representation the­ ory and the character theory of reductive groups over finite fields, and in the general modular representation theory of finite groups.

FUKUSHIMA (i) OP(G) = NXIH for some elementary abelian p-group N and a (p-radical) group H, where Op (G) is the minimal normal subgroup of G of index prime to p. (ii) H=MXP, where M is a p'-group and P is an elementary abelian p-group. (iii) P c MC H(x) for all xeN.

(4) The following conditions hold. (i) OP(G/ O p(G)) = G 0xN 0, where N o is an elementary abelian p-group and.

p-singular weights to p-regular weights to obtain some results on the Loewy series of certain modules for Frobenius subgroups.

The representation theory of complex semisimple Lie algebras is an important source of methods in the representation theory of algebraic groups over fields of prime characteristic.

These two theories are somehow parallel. In the former case, the next projective cover is and the resolution terminates with projective dimension 3, but in the latter case the resolution terminates immediately with projective dimension 2. The former case “uses” the 4 from leaving from and from.

The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems.

Essentially, the Krull-Schmidt Theorem holds for some classes of modules Author: Alberto Facchini. '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.In section 2, we study the injective and projective modules in the truncated cate-gory. The structure of the projective modules can be obtained from that of injective modules via the duality functor.

So we concentrate on the injective modules. We prove that the indecomposable injective modules have a “good” filtration and the so-called.projective modules is called an nth module of syzygies of M. Equvialently, an nth module of syzygies may be de ned recursively as a rst module of syzygies of any n 1st module of syzygies.

Note that the (usually in nite) sequence ()! P n!P n 1!! P 3!P 2!P 1!P 0!M!0 is exact as well, and so is a projective File Size: KB.