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In the 1980s, however, Jerry Fodor revived the idea of the modularity of mind, although without the notion of precise physical localizability. Drawing from Noam Chomsky's idea of the language acquisition device and other work in linguistics as well as from the philosophy of mind and the implications of optical illusions, he became a major proponent of the idea with the 1983 publication of ...
For example, the vertex of each indecomposable module in a block is contained (up to conjugacy) in the defect group of the block, and no proper subgroup of the defect group has that property. Brauer's first main theorem states that the number of blocks of a finite group that have a given p -subgroup as defect group is the same as the ...
It contains the modular group PSL(2, Z). Also closely related is the 2-fold covering group, Mp(2, R), a metaplectic group (thinking of SL(2, R) as a symplectic group). Another related group is SL ± (2, R), the group of real 2 × 2 matrices with determinant ±1; this is more commonly used in the context of the modular group, however.
In mathematics, a group is called an Iwasawa group, M-group or modular group if its lattice of subgroups is modular. Alternatively, a group G is called an Iwasawa group when every subgroup of G is permutable in G (Ballester-Bolinches, Esteban-Romero & Asaad 2010, pp. 24–25). Kenkichi Iwasawa proved that a p-group G is an Iwasawa group if and ...
In mathematics, the modular group is the projective special linear group (,) of matrices with integer coefficients and determinant, such that the matrices and are identified. The modular group acts on the upper-half of the complex plane by linear fractional transformations .
Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group () ().
Some examples of cognitive modules: The modules controlling your hands when you ride a bike, to stop it from crashing, by minor left and right turns. The modules that allow a basketball player to accurately put the ball into the basket by tracking ballistic orbits. [7] The modules that recognise hunger and tell you that you need food. [8]
A group is called unimodular if the modular function is identically , or, equivalently, if the Haar measure is both left and right invariant. Examples of unimodular groups are abelian groups, compact groups, discrete groups (e.g., finite groups), semisimple Lie groups and connected nilpotent Lie groups.