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Group Homomorphism and Isomorphism
We introduce the notion of homomorphism of groups as a map between two groups which respects the group structure so that we may establish...
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Group Homomorphisms and Isomorphic Groups
In this chapter, maps between two groups called homomorphisms are presented and discussed . The bijective versions of these maps, isomorphisms, are...
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On a group extension involving the Suzuki group Sz(8)
The Suzuki simple group Sz (8) has an automorphism group 3. Using the electronic Atlas [
22 ], the group Sz (8) : 3 has an absolutely irreducible module... -
Group Theory and Sage
At present, almost no mathematician works without using software. Software such as MATLAB and MATHEMATICA are among the best tools for engineers and...
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The Dixmier–Douady class, the action homomorphism, and group cocycles on the symplectomorphism group
Let X be a one-connected and integral symplectic manifold. In this paper, we construct and study a two-cocycle and three-cocycle on the...
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Compact Group Actions and Boundaries
Geometric group theory is devoted to the interplay between the algebraic structure of a group and properties of its actions on geometric and...
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Specht Modules and Representations of Symmetric Group
The symmetric group plays a key role in many areas of research in addition to mathematics and hence is of great importance. It is well known that...
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Permutation Group and the Determinant
Let us design a new group: the group of permutations. It will help define the determinant in a new way. This will give us a few attractive...
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Group invariant variational principles
In this paper we introduce a group invariant version of the well-known Ekeland variational principle. To achieve this, we define the concept of...
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Group of Units of Finite Group Algebras for Groups of Order 24
Let F be a finite field of characteristic p. The structures of the unit groups of group algebras over F for the three groups D 24 , S 4 and SL (2, ℤ 3 ) of...
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Equivariant Map** Class Group and Orbit Braid Group
Motivated by the work of Birman about the relationship between map** class groups and braid groups, the authors discuss the relationship between...
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Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group
For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore...
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The étale fundamental group of moduli of parahoric group scheme torsors over a curve
Let X be a smooth projective curve over an algebraically closed field k . Let G be an almost simple simply-connected group over k . Let
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The Symmetric Group
This part will be devoted to the study of partially symmetric functions: functions that are symmetric in some variables, while not necessarily being...
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Optimization of Group Incentive Schemes
AbstractThis paper considers the problem of motivating the reduction of project duration. The duration cuts of project works and the corresponding...
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Fractals via Self-Similar Group of Fisher Contractions
The fractal notion was unveiled by Mandelbrot in 1975, and a number of researchers continued to popularize the fractal theory. The chaotic structures...
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Prym representations of the handlebody group
Let S be an oriented, closed surface of genus g . The map** class group of S is the group of orientation preserving homeomorphisms of S modulo...
