[PDF] Top 20 Computing with simple groups: maximal subgroups and presentations
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Computing with simple groups: maximal subgroups and presentations
... each maximal subgroup of G can be , generated by two elements of G with the exception of a maximal subgroup of A7 of order ...each maximal subgroup M of G in its generators the conjugacy classes of G ... See full document
208
Algorithms for Computing Restricted Root Systems and Weyl Groups
... g simple defined over a field k which is algebraically closed, the real numbers, the p-adic numbers, a finite field or a number field there are 45 different types of Γ -indices which are absolutely ...the ... See full document
152
Triple factorization of non-abelian groups by two maximal subgroups
... proper subgroups of G, defined and studied by Gorenstein ([8]) in 1962 and the notation T = (G, A, B) is used for a triple factorization of the group ...Frobenius groups is studied. In 1990 the factor- ... See full document
9
The number of maximal subgroups and probabilistic generation of finite groups
... a simple group G that generate G also tends to infinity as |G| tends to ...almost simple group with socle S, the probability that a pair of elements of G generates a subgroup containing S tends to 1 as | G ... See full document
12
The maximal subgroups of the classical groups in dimension 13, 14 and 15
... the maximal subgroups of specific classical groups was Peter ...the maximal subgroups of the simple classical groups in dimension up to ...the maximal ... See full document
201
Symmetric Presentations, Representations, and Related Topics
... first order relations to obtain finite homomorphic images of simple groups. That is, we factor by the smallest normal subgroups to obtain these images. Since the conju- gacy classes are normal, we ... See full document
200
Simple irreducible subgroups of exceptional algebraic groups
... these maximal subgroups M , we find all simple M -irreducible subgroups of rank at least 2 and call these “candidate” ...candidate subgroups are G-irreducible, and to solve the ... See full document
47
SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS
... sporadic groups. We wrote such progenitors on many groups with no thinking behind the choice of our control ...is simple and thus is generated by involutions (Feit Thompson ...was simple, ... See full document
168
Groups With Two Generators Having Unsolvable Word Problem And Presentations of Mihailova Subgroups
... Novikov [35] and Boone [4] independently proved that there is a finitely presented group having un- solvable word problem. In 1969, Borisov [6] gave an elegant simplification on Boone’s approach. Then in 1986, applying ... See full document
13
Maximal subgroups of classical groups in dimensions 16 and 17
... the maximal subgroups must satisfy, but do not (in their original statement) describe precisely what the maximal subgroups ...almost simple groups, which is often relatively ... See full document
263
Presentations : from Kac Moody groups to profinite and back
... In the proof below, an important argument is the fact that the Steinberg version of a celebrated theorem of Curtis and Tits holds over rings. This result was announced almost 40 years ago by R.K. Dennis and M.R. Stein ... See full document
24
All simple groups with order from 1 million to 5 million are efficient
... As far as reliability of results is concerned we assert that all presentations given in this paper correctly define the groups. Each new presentation which appears has been verified by both GAP and Magma ... See full document
14
Symmetric Presentations of Coxeter Groups
... the presentations considered in this ...symmetric presentations of the main theorem to construct real representations of the groups con- cerned and, in doing so, complete the ... See full document
17
On the Number of Distinct Fuzzy Subgroups for Some Elementary Abelian Groups and Quaternion Groups
... fuzzy subgroups of Z p × Z p and the number of chains of subgroups of Z p × Z p that ends in Z p × Z p fixed for a particular element f k ∈ Aut( Z p × Z p ... See full document
7
Endomorphisms of Fraïssé limits and automorphism groups of algebraically closed relational structures
... In this chapter we consider the well known total order Q . We will find that it is a great deal more complicated to determine the maximal subgroups of End( Q ). We will first show that we can characterise ... See full document
170
On maximal subgroups of free idempotent generated semigroups
... a maximal sub- group of some free idempotent generated ...a maximal subgroup of some free idempotent gen- erated semigroup arising from a finite ...a maximal subgroup of some free regular idempotent ... See full document
27
Balanced subgroups of Abelian groups
... compact groups of Kaplansky [1]. These groups are well known and are in fact characterised by isomorphism ...free groups are seen to be the cotorsion groups of Harrison ... See full document
120
An introduction to the tools hosted in the Bilbao Crystallographic Server
... group number and the transformation matrix (P, p). Additional metrical conditions restrict the list of possible supergroups for structures of triclinic and monoclinic symmetry. Depending on the type of search, single or ... See full document
22
Centralizers in simple locally finite groups
... in simple finite groups to the structure in the centralizers of elements in ...finite groups and the extension of this to the groups which has this property ...finite groups having a ... See full document
10
The maximal subgroups of the unitary group PSU(6, q), where q=2^k
... In this section, we will consider the minimal normal subgroup M of H is not abelian and a finite primitive subgroup of rank three, so will use the classification of Kantor and Liebler {Result 4.2.2} for the primitive ... See full document
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