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  2. Vertical dyad linkage theory - Wikipedia

    en.wikipedia.org/wiki/Vertical_Dyad_Linkage_Theory

    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.

  3. Leader–member exchange theory - Wikipedia

    en.wikipedia.org/wiki/Leader–member_exchange...

    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 ...

  4. Leadership - Wikipedia

    en.wikipedia.org/wiki/Leadership

    LMX theorizes that the type of exchanges between the leader and specific followers can lead to the creation of in-groups and out-groups. In-group members are said to have high-quality exchanges with the leader, while out-group members have low-quality exchanges with the leader. [79]

  5. Word (group theory) - Wikipedia

    en.wikipedia.org/wiki/Word_(group_theory)

    In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]

  6. List of small groups - Wikipedia

    en.wikipedia.org/wiki/List_of_small_groups

    Dih n: the dihedral group of order 2n (often the notation D n or D 2n is used) K 4: the Klein four-group of order 4, same as Z 2 × Z 2 and Dih 2; D 2n: the dihedral group of order 2n, the same as Dih n (notation used in section List of small non-abelian groups) S n: the symmetric group of degree n, containing the n! permutations of n elements ...

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  8. Order (group theory) - Wikipedia

    en.wikipedia.org/wiki/Order_(group_theory)

    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 | .

  9. Presentation of a group - Wikipedia

    en.wikipedia.org/wiki/Presentation_of_a_group

    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.

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