Accounts for the groups SL(2,U), U = 41 and 43

The circular retail for the groups (2,) where = 41 and 43 compute in this paper from the ordinary character table and the character table (ch.t.) of rational representations (r.rep.) for each group.

Cyclic partition for the groups of PSL(2,41) and PSL(2,43)

The ordinary character table and the character table (cha.ta.) of rational representations (ra.repr.) for projective special linear groups (2,41) and (2,43) find in this work to find the cyclic partition for each group

Introduction

The introduction presents the main arguments of the book and the theoretical and historical background guiding the analysis, proposing a shift in approaches to artificial intelligence on the basis of a new assumption: that what machines are changing is primarily us: humans. It introduces the concept of “banal deception,” which describes deceptive mechanisms and practices that are embedded in media technologies and contribute to their integration into everyday life. Five key characteristics of banal deception are outlined and discussed: first, its everyday and ordinary character; second, its functionality and the fact that it always has some potential value to the user; third, its obliviousness, or the fact that the deception is not understood as such but taken for granted; fourth, its low definition, which refers to the fact that it demands participation from users in the construction of sense; and fifth, that banal deception is not just imposed on users but also “programmed” by designers and developers.

On a two-fold cover 2.(2⁶˙G₂(2)) of a maximal subgroup of Rudvalis group Ru

The Schur multiplier M(Ḡ1) ≅4 of the maximal subgroup Ḡ1 = 2⁶˙G₂(2)of the Rudvalis sporadic simple group Ru is a cyclic group of order 4. Hence a full representative group R of the type R = 4.(2⁶˙G₂(2)) exists for Ḡ1. Furthermore, Ḡ1 will have four sets IrrProj(Ḡ1;αi) of irreducible projective characters, where the associated factor sets α1, α2, α3 and α4, have orders of 1, 2, 4 and 4, respectively. In this paper, we will deal with a 2-fold cover 2. Ḡ1 of Ḡ1 which can be treated as a non-split extension of the form Ḡ = 27˙G2(2). The ordinary character table of Ḡ will be computed using the technique of the so-called Fischer matrices. Routines written in the computer algebra system GAP will be presented to compute the conjugacy classes and Fischer matrices of Ḡ and as well as the sizes of the sets |IrrProj(Hi; αi)| associated with each inertia factor Hi. From the ordinary irreducible characters Irr(Ḡ) of Ḡ, the set IrrProj(Ḡ1; α2) of irreducible projective characters of Ḡ1 with factor set α2 such that α22= 1, can be obtained.

Transformation of the Classical genre: Quadratus and beginnings of Christian apology

Quadratus belonged to the second generation of Jesus’ followers. At the early stage of his life he was an itinerant preacher of the Gospel, also visiting Asia Minor in the course of his travels. It was there that he may have received information about the persons who had directly experienced Jesus’ beneficence. After he settled in Athens, Quadratus, just like other Athenian apologists, Aristides and, later, Athenagoras, was not part of the Church hierarchy, but, more likely, a free teacher. When Hadrian was visiting Athens, he was presented with an apology which should have provided the emperor with reliable information concerning the new religion. The paper suggests a hypothesis that the direct impulse to defend Christianity was the conflict between the Christians and the Athenian society on the issue of the Eleusinian mysteries.Quadratus’ apologetic opus, among other topics of which we have no knowledge, discussed the unique character of the miracles performed by Christ, comparing them to the deeds of the demigods or of the contemporary miracle-workers. It also (according Martyrologium of Bede the Venerable) discussed the nature of Christian food, emphasising its ordinary character. Just as the Letter to Diognetus, it probably suggested that the Christian way of life and customs were not different from those of other people.

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

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.

Robinson’s conjecture for classical groups

Robinson’s conjecture states that the height of any irreducible ordinary character in a block of a finite group is bounded by the size of the central quotient of a defect group. This conjecture had been reduced to quasi-simple groups by Murai. The case of odd primes was settled completely in our predecessor paper. Here we investigate the 2-blocks of finite quasi-simple classical groups.

On blocks with one modular character

Suppose that B is a Brauer p-block of a finite group G with a unique modular character φ. We prove that φ is liftable to an ordinary character of G (which moreover is p-rational for odd p). This confirms the basic set conjecture for these blocks.

On Real and Rational Characters in Blocks

The principal $p$-block of a finite group $G$ contains only one real-valued irreducible ordinary character exactly when $G/{{\bf O}_{p'}(G)}$ has odd order. For $p \ne 3$, the same happens with rational-valued characters. We also prove an analogue for $p$-Brauer characters with $p \geq 3$.