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[MathJax off]

# CRIME

## A GAP Package to Calculate Group Cohomology and Massey Products

1.6

17 March 2022

Marcus Bishop
Email: marcus.bishop@gmail.com
Homepage: http://math.uic.edu/~marcus

### Copyright

© 2006, 2007 Marcus Bishop

CRIME is free software which is distributed under the GNU Public Licence, version 2, and may be redistributed under the GNU Public Licence, version 2 or later (at your preference). See the file COPYING for detailed information

### Acknowledgements

This project would not have been possible without Jon Carlson. Jon devised the algorithms used by `ProjectiveResolution`, `CohomologyGenerators`, and `CohomologyRelators`, having already implemented them in Magma, and shared these programs with me.

### Contents

1 Introduction
1.1 Installation and Loading
1.2 For Further Information
2 Usage
2.1 Cohomology Objects
2.1-1 CohomologyObject
2.2 Minimal Projective Resolutions
2.2-1 ProjectiveResolution
2.2-2 BoundaryMap
2.3 Cohomology Generators and Relators
2.3-1 CohomologyGenerators
2.3-2 CohomologyRelators
2.4 Tests for Completion
2.5 Cohomology Rings
2.5-1 CohomologyRing
2.5-2 IsHomogeneous
2.5-3 Degree
2.5-4 LocateGeneratorsInCohomologyRing
2.6 What Happens if `n` Isn't Big Enough?
2.7 Induced Maps
2.7-1 InducedHomomorphismOnCohomology
2.7-2 SubgroupInclusion
2.8 Massey Products
2.8-1 MasseyProduct
A Some Benchmarks
B Leisure and Recreation: Cohomology Rings of all Groups of Size 16
References
Index
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