The maximal subgroups of the Lyons group

1985 ◽  
Vol 97 (3) ◽  
pp. 433-436 ◽  
Author(s):  
Robert A. Wilson
Keyword(s):  
Simple Group ◽  
Maximal Subgroups ◽  
Subgroup Structure ◽  
Image Position ◽  
Lyons Group

In this paper we complete the work begun in [2] on the subgroup structure of the Lyons simple group Ly of order

scholarly journals Maximal Subgroups and Irreducible Representations of Generalized Multi-Edge Spinal Groups

2018 ◽  
Vol 61 (3) ◽  
pp. 673-703 ◽  
Author(s):  
Benjamin Klopsch ◽  
Anitha Thillaisundaram
Keyword(s):  
Rooted Tree ◽  
Maximal Subgroups ◽  
Irreducible Representations ◽  
Prime Field ◽  
Infinite Dimensional ◽  
Special Cases ◽  
Profinite Completions ◽  
Spinal Group ◽  
Groups Acting On Trees ◽  
Image Position

AbstractLet p ≥ 3 be a prime. A generalized multi-edge spinal group $$G = \langle \{ a\} \cup \{ b_i^{(j)} {\rm \mid }1 \le j \le p,\, 1 \le i \le r_j\} \rangle \le {\rm Aut}(T)$$ is a subgroup of the automorphism group of a regular p-adic rooted tree T that is generated by one rooted automorphism a and p families $b^{(j)}_{1}, \ldots, b^{(j)}_{r_{j}}$ of directed automorphisms, each family sharing a common directed path disjoint from the paths of the other families. This notion generalizes the concepts of multi-edge spinal groups, including the widely studied GGS groups (named after Grigorchuk, Gupta and Sidki), and extended Gupta–Sidki groups that were introduced by Pervova [‘Profinite completions of some groups acting on trees, J. Algebra310 (2007), 858–879’]. Extending techniques that were developed in these more special cases, we prove: generalized multi-edge spinal groups that are torsion have no maximal subgroups of infinite index. Furthermore, we use tree enveloping algebras, which were introduced by Sidki [‘A primitive ring associated to a Burnside 3-group, J. London Math. Soc.55 (1997), 55–64’] and Bartholdi [‘Branch rings, thinned rings, tree enveloping rings, Israel J. Math.154 (2006), 93–139’], to show that certain generalized multi-edge spinal groups admit faithful infinite-dimensional irreducible representations over the prime field ℤ/pℤ.

The Arithmetic of the Quasi-Uniserial Semigroups without Zero

1971 ◽  
Vol 23 (3) ◽  
pp. 507-516 ◽  
Author(s):  
Ernst August Behrens
Keyword(s):  
Simple Semigroup ◽  
Disjoint Union ◽  
Maximal Subgroups ◽  
Ordered Semigroup ◽  
Partially Ordered ◽  
Completely Simple Semigroup ◽  
Image Position ◽  
Previous Paragraph ◽  
Completely Simple ◽  
Identity Elements

An element a in a partially ordered semigroup T is called integral ifis valid. The integral elements form a subsemigroup S of T if they exist. Two different integral idempotents e and f in T generate different one-sided ideals, because eT = fT, say, implies e = fe ⊆ f and f = ef ⊆ e.Let M be a completely simple semigroup. M is the disjoint union of its maximal subgroups [4]. Their identity elements generate the minimal one-sided ideals in M. The previous paragraph suggests the introduction of the following hypothesis on M.Hypothesis 1. Every minimal one-sided ideal in M is generated by an integral idempotent.

scholarly journals The Projective Character Tables of a Solvable Group 26:6×2

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Abraham Love Prins
Keyword(s):  
Simple Group ◽  
Soluble Group ◽  
Galois Field ◽  
Maximal Subgroups ◽  
Finite Soluble Group ◽  
Character Tables ◽  
Extension Group ◽  
Projective Character ◽  
Ordinary Character ◽  
Clifford Theory

The Chevalley–Dickson simple group G24 of Lie type G2 over the Galois field GF4 and of order 251596800=212.33.52.7.13 has a class of maximal subgroups of the form 24+6:A5×3, where 24+6 is a special 2-group with center Z24+6=24. Since 24 is normal in 24+6:A5×3, the group 24+6:A5×3 can be constructed as a nonsplit extension group of the form G¯=24·26:A5×3. Two inertia factor groups, H1=26:A5×3 and H2=26:6×2, are obtained if G¯ acts on 24. In this paper, the author presents a method to compute all projective character tables of H2. These tables become very useful if one wants to construct the ordinary character table of G¯ by means of Fischer–Clifford theory. The method presented here is very effective to compute the irreducible projective character tables of a finite soluble group of manageable size.

S-Maximal Subgroups of πl(M3)

1972 ◽  
Vol 24 (3) ◽  
pp. 439-449
Author(s):  
C. D. Feustel
Keyword(s):  
Projective Plane ◽  
Maximal Subgroup ◽  
Piecewise Linear ◽  
Simplicial Complexes ◽  
Maximal Subgroups ◽  
Connected Surface ◽  
Image Position

Let M be a compact, connected, irreducible 3-manifold. Let S be a closed, connected, 2-manifold other than the 2-sphere or projective plane. Let f be a map of S into M such thatSuppose for every closed, connected surface S1 and every map g:S1 → M such that(1) is an injection,(1) Then we shall say that the subgroup is a surface maximal or S-maximal subgroup of π1(M). We may also say that the map f is S-maximal.Let M be an irreducible 3-manifold which does not admit any embedding of the projective plane. Then we shall say that M is p2-irreducible. Throughout this paper all spaces will be simplicial complexes and all maps will be piecewise linear.

The Möbius function of PSL(3,2p) for any prime p

2021 ◽  
pp. 1-25
Author(s):  
Martino Borello ◽  
Francesca Dalla Volta ◽  
Giovanni Zini
Keyword(s):  
Simple Group ◽  
Prime Number ◽  
Euler Characteristic ◽  
Prime Power ◽  
Subgroup Lattice ◽  
Möbius Function ◽  
Maximal Subgroups ◽  
Order Complex ◽  
Combinatorial Objects ◽  
Mobius Function

Let [Formula: see text] be the simple group [Formula: see text], where [Formula: see text] is a prime number. For any subgroup [Formula: see text] of [Formula: see text], we compute the Möbius function [Formula: see text] of [Formula: see text] in the subgroup lattice of [Formula: see text]. To this aim, we describe the intersections of maximal subgroups of [Formula: see text]. We point out some connections of the Möbius function with other combinatorial objects, and, in this context, we compute the reduced Euler characteristic of the order complex of the subposet of [Formula: see text]-subgroups of [Formula: see text], for any prime [Formula: see text] and any prime power [Formula: see text].

A Note on Supersoluble Groups

1971 ◽  
Vol 23 (3) ◽  
pp. 562-564 ◽  
Author(s):  
D. L. Johnson
Keyword(s):  
Abelian Group ◽  
Prime Power ◽  
Maximal Subgroups ◽  
Prime Power Order ◽  
Supersoluble Groups ◽  
Representations Of Groups ◽  
Image Position

Let H be a subgroup of a group G (all groups considered throughout this article are finite); then H will be called primitive if the subgroupis distinct from H. Such subgroups, which are also called meet-irreducible, arise naturally in connection with minimal permutation representations of groups and in other contexts; for example, every subgroup of a group G can be written as an intersection of primitive subgroups of G, and the set of all primitive subgroups of G is characterized by its minimality with respect to this property. While maximal subgroups are always primitive, most groups contain non-maximal subgroups which are primitive (see remark at end of article). Note that a subgroup H of an abelian group G is primitive if, and only if, G/H is cyclic of prime-power order.

The Schur Subgroup of a p-Adic Field

1979 ◽  
Vol 31 (2) ◽  
pp. 300-303
Author(s):  
Eugene Spiegel ◽  
Allan Trojan
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Group Algebras ◽  
Brauer Group ◽  
Ramification Index ◽  
Simple Component ◽  
Image Position ◽  
Cyclotomic Algebras ◽  
A Finite Group ◽  
Tame Ramification

Let K be a field. The Schur subgroup, S(K), of the Brauer group, B(K), consists of all classes [△] in B(K) some representative of which is a simple component of one of the semi-simple group algebras, KG, where G is a finite group such that char K ∤ G. Yamada ([11], p. 46) has characterized S(K) for all finite extensions of the p-adic number field, Qp. If p is odd, [△] ∈ S(K) if and only ifwhere c is the tame ramification index of k/Qp, k the maximal cyclotomic subfield of K, and s = ((p – 1)/c, [K : k]). invp △ is the Hasse invariant. Yamada showed this by proving first that S(K) is the group of classes containing cyclotomic algebras and then determining the invariants of such algebras.

scholarly journals Corrigendum

1988 ◽  
Vol 103 (2) ◽  
pp. 383-383
Author(s):  
Peter B. Kleidman ◽  
Robert A. Wilson
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Maximal Subgroups ◽  
Sporadic Simple Group ◽  
Computer Calculations

Volume 102 (1987), 17–23‘The maximal subgroups of Fi22’We reported on some computer calculations which we used to complete the enumeration of the maximal subgroups of the sporadic simple group Fi22 and of its automorphism group Fi22:2. Unfortunately there was an error in these calculations. We have therefore repeated all the calculations, incorporating much more thorough checking routines.

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