Reductive groupIn mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n).
Solvable groupIn mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation. Specifically, a polynomial equation is solvable in radicals if and only if the corresponding Galois group is solvable (note this theorem holds only in characteristic 0).
Access-control listIn computer security, an access-control list (ACL) is a list of permissions associated with a system resource (object or facility). An ACL specifies which users or system processes are granted access to resources, as well as what operations are allowed on given resourcess. Each entry in a typical ACL specifies a subject and an operation. For instance, If a file object has an ACL that contains , this would give Alice permission to read and write the file and give Bob permission only to read it.
Group theoryIn abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Computer fileIn computing, a computer file is a resource for recording data on a computer storage device, primarily identified by its . Just as words can be written on paper, so can data be written to a computer file. Files can be shared with and transferred between computers and mobile devices via removable media, networks, or the Internet. Different are designed for different purposes. A file may be designed to store an , a written message, a video, a program, or any wide variety of other kinds of data.
Microsoft WindowsMicrosoft Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for servers, and Windows IoT for embedded systems. Defunct Windows families include Windows 9x, Windows Mobile, and Windows Phone. The first version of Windows was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs).
ChmodIn Unix and Unix-like operating systems, is the command and system call used to change the and the special mode flags (the setuid, setgid, and sticky flags) of objects ( and directories). Collectively these were originally called its modes, and the name was chosen as an abbreviation of change mode. A command first appeared in AT&T UNIX version 1, along with the system call. As systems grew in number and types of users, access-control lists were added to many file systems in addition to these most basic modes to increase flexibility.
File managerA file manager or file browser is a computer program that provides a user interface to manage and folders. The most common performed on files or groups of files include creating, opening (e.g. , playing, editing or printing), renaming, , , and searching for files, as well as modifying s, properties and . Folders and files may be displayed in a hierarchical tree based on their directory structure. Graphical file managers may support copying and moving of files through "copy and paste" and "cut and paste" respectively, as well as through drag and drop, and a separate menu for selecting the target path.
Automorphism groupIn mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.
Dihedral groupIn mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, D_n or Dih_n refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D_2n refers to this same dihedral group.
Abelian groupIn mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.
Files-11Files-11 is the used in the RSX-11 and OpenVMS operating systems from Digital Equipment Corporation. It supports record-oriented I/O, remote network access, and . The original ODS-1 layer is a ; the ODS-2 version is a , with support for access control lists,. Files-11 is similar to, but significantly more advanced than, the file systems used in previous Digital Equipment Corporation operating systems such as TOPS-20 and RSTS/E. The native OpenVMS file system is descended from older DEC operating systems and is similar in many ways, both having been designed by Dave Cutler.
