# cohomolo

Cohomology groups of finite groups on finite modules

Version 1.6.8
Released 2019-07-07

This project is maintained by The GAP Team

# The GAP 4 package ‘cohomolo’

## Package description

It may be used to perform certain cohomological calculations on a finite permutation group G. The following properties of G can be computed:

1. The p-part Mul_p of the Schur multiplier Mul of G, and a presentation of a covering extension of Mul_p by G, for a specified prime p;

2. The dimensions of the first and second cohomology groups of G acting on a finite dimensional KG-module M, where K is a field of prime order; and

3. Presentations of split and nonsplit extensions of M by G.

## Installation

This package uses external binaries and currently works only under UNIX/LINUX systems.

To install the package go to the GAP directory pkg/cohomolo (the directory containing this README file) and call

./configure PATH


where PATH is a path to the main GAP root directory; so normally you would call

./configure ../..


and then call

make


to compile the binary.

If you installed GAP on several architectures, you must execute this configure/make step for the cohomolo package on each of the architectures immediately after configuring GAP itself on this architecture.

## Documentation

Full information and documentation can be found in the manual, available as PDF doc/manual.pdf or as HTML htm/chapters.htm, or on the package homepage at

https://gap-packages.github.io/cohomolo/

## Bug reports and feature requests

Please submit bug reports and feature requests via our GitHub issue tracker:

https://github.com/gap-packages/cohomolo/issues

This package has been updated from the original GAP3 package with minimal changes, so the user should find the interface unchanged. In fact the only real changes are that the function InfoCohomology has been replaced by the Info variable InfoCohomolo, and the function SplitExtension has been renamed `SplitExtensionCHR, to avoid clashing with an existing GAP function name. (Of course, it does more or less the same thing as the GAP function!)