# On Primitive Representations Of Soluble Groups Of Finite Rank

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### University of Warwick institutional repository: http://go

a cyc:lic intersection supplement, then G. is soluble and has rank at most 2. Also, if G is a finite soluble group in which every subgroup has an abelian. intersection supple ment, then. G has derived length at most 4. If TI is a set of prime numbers, then the study of finite groups in which

### Cumulative Author-Title Index for Volumes 98-104

Special Linear Groups by Transvections, 99, [email protected] HUNEKA, C ANV Rossr. M The Dimension and Components of Symmetric Algebras, 98. [email protected] IO. HUNT, DAVID C Rational Rigidity and the Sporadic Groups, 99, 577-592. HUPPERT. BERTKAM. Solvable Groups. All of Whose Irreducible Representations in

### Groups St Andrews: Full Academic and Social Timetable

groups 12.00 Natalia Makarenko, Finite groups with a metacyclic Frobenius group of automorphisms Robert Shwartz, Counting cyclic indentities in speci c nite groups Nathan Corwin, A non-embedding result for R. Thompson s group V Andrew Douglas, Classi cation of embeddings of abelian extensions of D n into E n+1

### Conjugacy classes in the weyl group - Numdam

as reflection groups. It is desirable to do this in view of the importance of the Weyl groups in the theories of Lie groups, Lie algebras and algebraic groups. We shall give such a unified description of the conjugacy classes in the present paper - for the irreducible representations the problem remains open.

### ON SPINOR EXCEPTIONAL REPRESENTATIONS

Every spinor exceptional lattice K for G induces a primitive spinor exceptional lattice. Proof, There is an Ze(? which represents K. Let Y be a sublattice of X isometric to K, If T is the set of primes p at which Y p is imprimitive in X 9, then T is a finite set. For each p e T embed Y p in a primitive sub-lattice Y p of the same rank

### Abstracts of invited speakers talks

permutable subgroups of G, then fT is, respectively, the class of T-groups, PT-groups, or PST-groups. Let Fbe a formation of nite groups containing all nilpotent groups such that any normal subgroup of any fT-group in Fand any subgroup of any soluble fT-group in Fbelongs to F. A subgroup Mof a nite group Gis said to be F-normal in Gif G=Core

### Curriculum vitae Bijan Taeri

16. S. H. Shojaee, (2007) Primitive Elements With Zero Traces, (Supervisor) 17. H. Ahmadi, (2008) The Graph of Conjugacy Classes of Finite Groups, (Supervisor) 18. M. Arezoomandi, (2008) On the Linear Representations of Symmetry Groups of Single-wall carbon nanotubes, (Supervisor) 5

### Cumulative Author-Title Index for Volumes 120-I 27

Representations for Real Reductive Lie Groups I, 123, 289-236. CASSIDY, PHYLLIS JOAN, The Classification of the Semisimple Differential Algebraic Groups and the Linear Semisimple Dif- ferential Algebraic Lie Algebras, 121, 169-238. CHACRON, M., Correction to a Theorem on c-Ordering, 124, 23&23.5.

### ALEX BARTEL AND TIM DOKCHITSER If G X,Y ∼= G arXiv:1103

5. Primitive relations in p-groups 12 6. Main reduction in soluble groups 13 7. Quasi-elementary groups 17 7.1. The kernel of the conjugation action 18 7.2. Some Brauer relations 21 7.3. Primitive relations with trivial K 26 7.4. Primitive relations with non-trivial K 28 8. Examples 35 9. An application to regulator constants 35 References 38

### On element orders in covers of finite simple classical groups

In the following theorem, we do the same for the other classical groups (observe that the twisted rank of U5(2) 2A4(2) isequal to 2). Theorem 1. Let G be one of the simple groups Un(q),wheren4,S2n(q),wheren3,O2n+1(q),where n 3,andO± 2n (q),wheren4. Suppose that V is a G-module over a ﬁeld of characteristic r prime to q. Then

### Author Index Volume 88 (1993) - COnnecting REpositories

Collins, D.J. and E.C. Turner, An automorphism of a free group of finite rank with maximal rank fixed point subgroup fixes a primitive element Dicks. W. and E. Ventura, Irreducible automorphisms of growth rate one Dunwoody, M.J Inaccessible groups and protrees Gilchrist, A.J. and B. Hartley.

### ,'(17,7,(6,1$/02671,/327(17/,(5,1*6 LATTICES OF VARIETIES OF

Jul 27, 2019 COROLLARY 2. // a Lie ring L possesses a nilpotent ideal Ν of finite index such that every operator of the form ad χ, χ G L, is nilpotent on N, then L is finitely based. For soluble rings, nilpotence of the above operators can be weakened to being algebraic. COROLLARY 3. Every soluble almost nilpotent algebraic Lie ring is finitely based.

### UKRAINIAN MATHEMATICAL CONGRESS

Prime spectrum and primitive Leavitt path Modules over group rings of locally soluble groups with rank restrictions on Finite p-groups (p6= 2) with non

### Groups in supersimple and pseudo nite theories

in the soluble case) for groups in S, in particular Theorem 1.1. It follows from Theorem 1.1(ii) that there is a good general description of groups in F(see e.g. Proposition 3.4), and the ne structure of such groups will (assuming CFSG) reduce to understanding soluble groups in F. We then in Section 4 investigate rank 2 groups in M. The aim is

### ON THE PRIMITIVE REPRESENTATIONS OF FINITELY GENERATED

in the class of soluble groups of ﬁnite rank with the maximal condition for normal subgroups only polycyclic groups may have faithful irreducible primitive representations over a ﬁeld of

### On induced modules over locally Abelian-by-polycyclic groups

Let G be a locally Abelian-by-policyclyc group of finite rank, let k be a field of zero characteristic and let M be an irreducible kG -module. Then End kGM is algebraic over k REFERENCES 1. Tushev, A. V. (2000). On primitive representations of soluble groups of finite rank. Sb. Mat., 191, No. 11,

### (+ 1) (d -) ifp is any other prime. - JSTOR

In fact there exist examples for all primes p of p-soluble groups G with a p-block B, of defect d, containing an ordinary character of height exceeding (d- 1)/2. REFERENCES 1. R. Brauer, Some applications of the theory of blocks of characters of finite groups. IV, J. Algebra 17 (1971), 489-521. MR 43 # 7520. 2. R.

### by Klaus Doerk Trevor Hawkes

8. Finite nilpotent groups 25 9. The Frattini subgroup 30 10. Soluble groups 34 11. Theorems of Gaschiitz, Schur-Zassenhaus, and Maschke 38 12. Coprime operator groups 41 13. Automorphism groups induced on chief factors 44 14. Subnormal subgroups 47 15. Primitive finite groups 52 16. Maximal subgroups of soluble groups 57 17. The transfer 60 18

### Introduction

Such groups H are always reducible if n;m > 1. In fact, if H is an irreducible linear group, we show that, for every pair of non-zero vectors, their orbit lengths have a non-trivial common factor. In the more general context of nite primitive permutation groups G, we show that coprime non-identity subdegrees are possible if and only if G is of

### L(p, D), D

as studying the projective representations of the central quotient group. Finite subgroups ofGL(l, D) = D* were classified by Amitsur [1], so one may turn to finite subgroups of G L(p, D), where D is a division ring of characteristic zero, and p IS a pnme. Question 1. For what finite groups G is there a decomposition of the rational

### ResearchGate

1707 1748 02000 RAS(DoM) and LMS DOI On primitive representations of soluble groups of finite rank A. V. Tushev Abstract. the paper it is prcwed, in particular, that a group is polycyclic if

### On a conjecture of G.E. Wall - Imperial College London

For a finite groupG, let max(G) denote the number of maximal proper subgroups of G. In [33], Wall proves that max(G) ≤ G for soluble groups G, and conjectures that this is true for all finite groupsG. In [22, 4.6] this conjecture was verified for sufficiently large symmetric groups. In this paper we establish new bounds on max(G) for almost

### Symmetries of Discrete Objects - Auckland

A transitive permutation group has rank at least two, as the set of all pairs ( ; ) is an orbit. The rank two groups are the 2-transitive groups, and their classi cation was a consequence of the Classi cation of Finite Simple Groups. All 2-transitive groups are primitive, but it is not necessary for a rank three group to be primitive. All primitive

### arXiv:2010.04808v1 [math.GR] 9 Oct 2020

and the rank of G is G is soluble. The goal of this note is to answer these questions. First, we show that any nonabelian simple group can occur as a composition factor of some group with this property. It is perhaps remarkable that we do not need the classiﬁcation of ﬁnite simple groups to prove this. Theorem A.

### THE FINITE AND SOLUBLE GENUS OF A FINITELY

problem of existence of nitely generated residually-( nite soluble) groups with free prosoluble completion, show that the case k = 1 implies the general case and prove that it is enough to consider only nite soluble groups in the case k = d. 1. Introduction A nonempty class of groups Cis a formation if it is closed under taking homo-