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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.
Followership are the actions of someone in a subordinate role. It may also be considered as particular services that can help the leader, a role within a hierarchical organization, a social construct that is integral to the leadership process, or the behaviors engaged in while interacting with leaders in an effort to meet organizational objectives. [1]
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 | .
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 ...
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]
A presentation of a group determines a geometry, in the sense of geometric group theory: one has the Cayley graph, which has a metric, called the word metric. These are also two resulting orders, the weak order and the Bruhat order, and corresponding Hasse diagrams. An important example is in the Coxeter groups.
The Frobenius group of affine transformations of F 5 (maps + where a ≠ 0) has order 20 = (5 − 1) · 5 and acts on the field with 5 elements, hence is a subgroup of S 5. (Indeed, it is the normalizer of a Sylow 5-group mentioned above, thought of as the order-5 group of translations of F 5.)