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The theory focuses on types of leader-subordinate relationships [4] which are further classified into subgroups, namely the in-group and the out-group. [5] The in-group consists of members that receive greater responsibilities and encouragement, [5] and are able to express opinions without having any restrictions.
The leader–member exchange (LMX) theory is a relationship-based approach to leadership that focuses on the two-way relationship between leaders and followers. [1]The latest version (2016) of leader–member exchange theory of leadership development explains the growth of vertical dyadic workplace influence and team performance in terms of selection and self-selection of informal ...
The quality of the relationship between the two can be described by Sahin as a term called leader-member exchange (LMX) theory. What LMX theory basically points out against McGregor theory is that “leaders develop unique relationships with different subordinates and that the quality of these relationships is a determinant of how each ...
The order of a group G is denoted by ord(G) or | G |, and the order of an element a is denoted by ord(a) or | a |, instead of ( ), where the brackets denote the generated group. Lagrange's theorem states that for any subgroup H of a finite group G , the order of the subgroup divides the order of the group; that is, | H | is a divisor of | G | .
Transactional leaders pay attention to followers' work in order to find faults and deviations. A transactional leader follows the objective exchange of value between an employee's performance and the manager's response to it. The manager communicates clear requirements and goals to the employee and rewards achievements. [5]
For example, the dihedral group D 8 of order sixteen can be generated by a rotation, r, of order 8; and a flip, f, of order 2; and certainly any element of D 8 is a product of r ' s and f ' s. However, we have, for example, rfr = f −1 , r 7 = r −1 , etc., so such products are not unique in D 8 .
In geometric group theory, a graph of groups is an object consisting of a collection of groups indexed by the vertices and edges of a graph, together with a family of monomorphisms of the edge groups into the vertex groups. There is a unique group, called the fundamental group, canonically associated to each finite connected graph of
A similar construction gives the Hall–Janko group J 2 (order 604,800) as the quotient of the group of quaternionic automorphisms of Λ by the group ±1 of scalars. The seven simple groups described above comprise what Robert Griess calls the second generation of the Happy Family , which consists of the 20 sporadic simple groups found within ...