[Q]: Information: - In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup of a group is normal in if and only if for all in ; i.e., the sets of left and right cosets coincide. Normal subgroups (and "only" normal subgroups) can be used to construct quotient groups from a given group. - In mathematics, the general linear group of degree "n" is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible. The group is so named because the columns of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position. - Algebra (from Arabic ""al-jabr"" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. - In mathematics, matrix multiplication or the matrix product is a binary operation that produces a matrix from two matrices. The definition is motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering. In more detail, if is an matrix and is an matrix, their matrix product is an matrix, in which the entries across a row of are multiplied with the entries down a columns of and summed to produce an entry of . When two linear transformations are represented by matrices, then the matrix product represents the composition of the two transformations. - In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix. The determinant of a matrix is denoted det(), det , or ||. It can be viewed as the scaling factor of the transformation described by the matrix. - Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces. - In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term "abstract algebra" was coined in the early 20th century to distinguish this area of study from the other parts of algebra. - Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties , such as vector spaces , from the point of view of their effect on functions . Classically , the theory dealt with the question of explicit description of polynomial functions that do not change , or are invariant , under the transformations from a given linear group . For example , if we consider the action of the special linear group SLn on the space of n by n matrices by left multiplication , then the determinant is an invariant of this action because the determinant of A X equals the determinant of X , when A is in SLn . - In mathematics, the special linear group of degree "n" over a field "F" is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant - In mathematics, a square matrix is a matrix with the same number of rows and columns. An "n"-by-"n" matrix is known as a square matrix of order "n". Any two square matrices of the same order can be added and multiplied. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - In mathematics, and more specifically in abstract algebra, an algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Given the information, choose the subject and object entities that have the relation of 'part of'.
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[A]: invariant theory , mathematics

[Q]: Information: - Kitty Girls is a defunct all-female singing group formed in April 2007, by Cecille Carpio of Elan Models International and Jose Felix Dingcong of JLD Management, in the Philippines. Originally a quintet, the group consisted of Jocelyn Oxlade, Ayanna Oliva, Veronica Scott, Nicole Deen and Tanya Yuquimpo. In 2010, the group relaunched as a trio with Khai Lim joining Oxlade and Oliva. - Jocelyn Rose Oxlade (born 2 January 1984) is a Filipino-British singer, model and make up artist. She is a former member of the Kitty Girls. - Ayanna Oliva is a Filipina model , singer , dancer , DJ , and VJ . She is a member of the Kitty Girls . Given the information, choose the subject and object entities that have the relation of 'country of citizenship'.
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[A]:
ayanna oliva , philippines