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Tuesday, July 14, 2020 | History

4 edition of Frattini-like subgroups of finite groups found in the catalog.

Frattini-like subgroups of finite groups

by Marian Deaconescu

  • 75 Want to read
  • 5 Currently reading

Published by Harwood Academic Publishers, Distributed by STBS in Chur [Switzerland], New York, London .
Written in English

    Subjects:
  • Frattini subgroups.

  • Edition Notes

    Includes bibliographical references (p. 493-498).

    StatementMarian Deaconescu.
    SeriesMathematical reports,, v. 2, pt. 4, Mathematical reports (Chur, Switzerland) ;, v. 2, pt. 4.
    Classifications
    LC ClassificationsQA171 .D387 1986
    The Physical Object
    Paginationx p., p. 385-498 ;
    Number of Pages498
    ID Numbers
    Open LibraryOL2336162M
    ISBN 103718603039
    LC Control Number86226329

    thereby giving representations of the group on the homology groups of the space. If there is torsion in the homology these representations require something other than ordinary character theory to be understood. This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract Size: 1MB. Finite Groups (AMS Chelsea Publishing) 2nd Edition by Daniel Gorenstein (Author) ISBN ISBN Why is ISBN important? ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The digit and digit formats both work. Format: Hardcover.

    The problem of enumerating subgroups of a finite abelian group is both non-trivial and interesting. It is also worthwhile to study this set as a lattice. As far as I know, the reference "Subgroup lattices and symmetric functions" by Lynne M. Butler (Memoirs of the AMS, no. ; MR) reflects the state of g: Frattini-like. Symbol Meaning C n;q;1 n (1;q) cyclic group generated by " n 0 0 "qn D n;q dihedral group of order 4(n q)q T m tetrahedral group of order 24m O m octahedral group of order 48m I m icosahedral group of order m N p normal subgroup of a group Gwith order a power of a prime number p n p number of Sylow p-subgroups of a group G Z(G) center of a group G O x orbit Missing: Frattini-like.

    In group theory, a branch of abstract algebra, a cyclic group or monogenous group is a group that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its g: Frattini-like. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important g: Frattini-like.


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Frattini-like subgroups of finite groups by Marian Deaconescu Download PDF EPUB FB2

A class of Frattini-like subgroups of a finite group, Journal of Pure and Applied Algebra 78 () Let G be a finite group and 7r a set of primes. We consider the families of subgroups of G.a, _ {M: M G, IG: M1= 1}, 3== {M: M G, IG: M1= 1, IG: MI is composite}.Cited by: 5. Frattini-like subgroups of finite groups.

Chur [Switzerland] ; New York: Harwood Academic Publishers ; London: Distributed by STBS, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors /.

A class of Frattini-like subgroups of a finite group Yanming Wang Institute of Mathematics, Peking University, BeijingPeople’s Republic of China Communicated by K.W.

Gruenberg Received 6 January Revised 15 March Abstract Wang, Y., A class of Frattini-like subgroups of a finite group. The Frattini subgroup φ(G) of a group G is the intersection of G and all its maximal subgroups. The following results for finite groups are well known: THEOREM A0. If G is a finite group, then the following three conditions are equivalent: (i) G is nilpotent, (ii) G/φ(G) is nilpotent, (iii) φ(G) ≥ Frattini-like subgroups of finite groups book ′.Cited by: Deaconescu, M.

Frattini-like subgroups of finite groups, c p. ix (Frattini subgroups) found: Encyc. math. (Frattini subgroup: the characteristic subgroup of a group G defined as the intersection of all maximal subgroups of G). Following Gaschütz [10], we call a group φ-free if its Frattini subgroup is trivial.

We denote by the class of groups G such that is φ-free for all normal subgroups N of G. It is clear that a group if and only if G has no Frattini chief factors (recall that a chief factor of a group G is said to be Frattini Cited by: 1.

On the embedding of a finite group as Frattini subgroup de Nijs, Cynthia H. and van der Waall, Robert W., Bulletin of the Belgian Mathematical Society - Simon Stevin, ; Generalized Frattini subgroups of finite groups.

Beidleman, J. and Seo, T. K., Pacific Journal of Mathematics, ; Frattini subgroups and $\Phi $-central groups. relationship between the Frattini subgroup of the wreath product A Wr B of two groups A and B and that of A and F. For example Theorem 3. If A and B are finite groups of coprime order then Av/r B is i> free o A is $ free.

And on the other hand Theorem 4. If A and B are groups without maximal subgroups and A is abelian. In mathematics, the Frattini subgroup φ(G) of a group G is the intersection of all maximal subgroups of G.

For the case that G has no maximal subgroups, for example the trivial group e or the Prüfer group, it is defined by φ(G) = G.

It is analogous to. The set of orders of elements in a finite Abelian group is closed under taking least common multiples. (Edit: This happens to be the subject of another question. It may seem quite hard, unless one realises that in Abelian torsion groups, different prime factors can be considered independently due to a canonical direct sum decomposition, after which the Missing: Frattini-like.

Given such an f, let fT denote the class of finite groups in which f(G) is the set of subnormal subgroups of G; this is the class of all finite groups G in which to be in f(G) is a transitive.

Feng and B. Zhang, Frattini subgroups relative to formation functions, J. Pure Appl. Algebra 64 (), – Förster, On finite groups all of whose subgroups are 𝓕-subnormal or 𝓕subabnormal, J. Algebra (), – Griess and P. Schmid, The Frattini module, Arch.

Math. 30 (), – Cited by: In this paper, we show that G is a finite group in which every nonabelian subgroup is a TI-subgroup if and only if every nonabelian subgroup of G is normal in G. FINITE GROUPS IN WHICH ALL NONABELIAN SUBGROUPS ARE TI-SUBGROUPS | Journal of Cited by: 7.

Letting P be a p -group and φ(P) be the Frattini subgroup of P (the intersection of all maximal subgroups), the challenge is "Prove that P / N is elementary abelian implies φ(P) ≤ N " (from Dummit and Foote b).

The previous exercise has already established P / φ(P) is elementary abelian. "The monumental classification of finite simple groups, which occupies s pages spread over journal articles, is now complete, and the complete list of the finite simple groups has attracted wide Atlas brings together detailed information about these groups--their construction, character tables, maximal subgroups, and prefatory 5/5(1).

Let G be a finite group and H a subgroup of G. We say that H is an ℋ -subgroup of G if N G (H) ∩ H g ≤ H for all g ∈ G. We say that H is weakly ℋ 풞 -embedded in G if G has a normal subgroup T such that H G = H T and N T (H) ∩ H g ≤ H for all g ∈ G, where H G is the normal closure of H in by: 1.

In particular, if is a finite group and for some subgroup of, then. Using this observation, Frattini proved that the Frattini subgroup of a finite group is nilpotent (cf.

also Nilpotent group). This basic result gave its name. A class of Frattini-like subgroups of a finite group By Yanming Wang Download PDF ( KB)Author: Yanming Wang. X-semi permutable subgroups of finite groups Article (PDF Available) in Journal of Algebra (no.1,) May with 47 Reads How we measure 'reads'Missing: Frattini-like.

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups.

In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory Missing: Frattini-like.

The book contains: Groups, Homomorphism and Isomorphism, Subgroups of a Group, Permutation, and Normal Subgroups. The proofs of various theorems and examples have been given minute deals each chapter of this book contains complete theory and fairly large number of solved examples/5(3).solvable groups all of whose 2-local subgroups are solvable.

The reader will realize that nearly all of the methods and results of this book are used in this investigation. At least two things have been excluded from this book: the representation theory of finite groups and—with a few exceptions—the description of the finite simple Size: 1MB.Finite Groups of Order Less Than or Equal to This document contains additional material for the preprint: K.

Parattu, A. Wingerter, \Tribimaximal Mixing From Small Groups", arXiv InTab. 1below, we list the groups of order The rst column gives the GAP ID which is a label that uniquely identi es the group in GAP. The rst Missing: Frattini-like.