LeadershipLeadership, both as a research area and as a practical skill, encompasses the ability of an individual, group, or organization to "", influence, or guide other individuals, teams, or entire organizations. "Leadership" is a contested term. Specialist literature debates various viewpoints on the concept, sometimes contrasting Eastern and Western approaches to leadership, and also (within the West) North American versus European approaches. Some U.S.
Group actionIn mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.
Leadership studiesLeadership studies is a multidisciplinary academic field of study that focuses on leadership in organizational contexts and in human life. Leadership studies has origins in the social sciences (e.g., sociology, anthropology, psychology), in humanities (e.g., history and philosophy), as well as in professional and applied fields of study (e.g., management and education). The field of leadership studies is closely linked to the field of organizational studies.
Leadership styleA leadership style is a leader's method of providing direction, implementing plans, and motivating people. Various authors have proposed identifying many different leadership styles as exhibited by leaders in the political, business or other fields. Studies on leadership style are conducted in the military field, expressing an approach that stresses a holistic view of leadership, including how a leader's physical presence determines how others perceive that leader.
Trait leadershipTrait leadership is defined as integrated patterns of personal characteristics that reflect a range of individual differences and foster consistent leader effectiveness across a variety of group and organizational situations (Zaccaro, Kemp, & Bader, 2004; Zaccaro 2007). The theory of trait leadership is developed from early leadership research which focused primarily on finding a group of heritable attributes that differentiate leaders from nonleaders.
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.
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
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).
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.
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).
