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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 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.
A free group has a unique normal form i.e. each element in is represented by a unique reduced word. Proof. An elementary transformation of a word w ∈ G {\displaystyle w\in G} consists of inserting or deleting a part of the form a a − 1 {\displaystyle aa^{-1}} with a ∈ S ± {\displaystyle a\in S^{\pm }} .
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]
The basis for a free group is not uniquely determined. Being characterized by a universal property is the standard feature of free objects in universal algebra. In the language of category theory, the construction of the free group (similar to most constructions of free objects) is a functor from the category of sets to the category of groups.
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