Professor Dr. at University of Baghdad, College of Education for Pure Sciences Ibn AL-Haitham, Department of Mathematics
Editor in Journal of Kufa for Mathematics and Computer
Editor in Journal of University of Anbar for Pure Science (JUAPS)
Applied Algebra Homological Algebra Representation Theory Character Theory
B.Sc. (University of Baghdad, College of Education Ibn-Al-Haitham, Department of Mathematics, 30/6/1997)
M.Sc.(University of Technology, Applied Sciences Department , Mathematics branch, 10/7/2005)
Ph.D. (Mustansiriyah University, College of Science, Department of Mathematics, 27/5/2019)
A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.
For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.
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The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.
The problem of finding the cyclic decomposition (c.d.) for the groups ), where prime upper than 9 is determined in this work. Also, we compute the Artin characters (A.ch.) and Artin indicator (A.ind.) for the same groups, we obtain that after computing the conjugacy classes, cyclic subgroups, the ordinary character table (o.ch.ta.) and the rational valued character table for each group.
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The set of all (n×n) non-singular matrices over the field F this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension over the field F, denoted by . The determinant of these matrices is a homomorphism from into F* and the kernel of this homomorphism was the special linear group and denoted by Thus is the subgroup of which contains all matrices of determinant one.
The rational valued characters of the rational representations written as a linear combination of the induced characters for the groups discuss in this paper and find the Artin indicator for this group after study the rational valued characters of the rational representations and the induce
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In this work, we prove by employing mapping Cone that the sequence and the subsequence of the characteristic-zero are exact and subcomplex respectively in the case of partition (6,6,4) .
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