Publication

The socle of a projective Mackey functor for a p-group

2009
Journal Articles

Abstract

We study the simple subfunctors of indecomposable projective Mackey functors for a p-group P. Unlike the case of group algebras, the Mackey algebra is not in general self-injective. Thus, the socle of an indecomposable projective functor is not in general simple. We first show that the simple subfunctors of a projective functor P_{H,k}, where H

Official source

https://infoscience.epfl.ch/entities/publication/3bbaa93c-37eb-4d40-9668-a5382c6ddc65

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2009
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3bbaa93c-37eb-4d40-9668-a5382c6ddc65

About this result

Related concepts (32)

Elementary abelian group

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same order. This common order must be a prime number, and the elementary abelian groups in which the common order is p are a particular kind of p-group. A group for which p = 2 (that is, an elementary abelian 2-group) is sometimes called a Boolean group. Every elementary abelian p-group is a vector space over the prime field with p elements, and conversely every such vector space is an elementary abelian group.

P-group

In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p. Abelian p-groups are also called p-primary or simply primary. A finite group is a p-group if and only if its order (the number of its elements) is a power of p.

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).

Related publications (32)

The socle of a projective Mackey functor for a p-group

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