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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 ...
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 .
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 ...
A modular function is a function that is invariant with respect to the modular group, but without the condition that it be holomorphic in the upper half-plane (among other requirements). Instead, modular functions are meromorphic : they are holomorphic on the complement of a set of isolated points, which are poles of the function.
The Modular Cognition Framework (MCF) is an open-ended theoretical framework for research into the way the mind is organized. It draws on the common ground shared by contemporary research in the various areas that are collectively known as cognitive science and is designed to be applicable to all these fields of research.
A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K). Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class.
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 ...
The modular function is a continuous group homomorphism from G to the multiplicative group of positive real numbers. 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 ...