On the covering number of small symmetric groups and some sporadic simple groups
-
Luise-Charlotte Kappe
Abstract
A set of proper subgroups is a cover for a group if its union is the whole group. The minimal number of subgroups needed to cover G is
called the covering number of G, denoted by
Funding source: Australian Research Council
Award Identifier / Grant number: DP120101336
Funding statement: The third author acknowledges the support of the Australian Research Council Discovery Grant DP120101336 during his time spent at The University of Western Australia.
Acknowledgements
We are very thankful to Eric Borenstein, the administrator of the High Performance Computing Initiative at Florida Atlantic University, for gaining us access to KoKo and for helping us implement Gurobi on KoKo, which included finding the best parameters for optimal performance. Finally, we would like to thank Gordon Royle for giving us access to his machine at The University of Western Australia.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Computing discrete logarithms using 𝒪((log q)2) operations from {+,-,×,÷,&}
- A parallel evolutionary approach to solving systems of equations in polycyclic groups
- Authenticated commutator key agreement protocol
- On the covering number of small symmetric groups and some sporadic simple groups
- Compositions of linear functions and applications to hashing
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Articles in the same Issue
- Frontmatter
- Computing discrete logarithms using 𝒪((log q)2) operations from {+,-,×,÷,&}
- A parallel evolutionary approach to solving systems of equations in polycyclic groups
- Authenticated commutator key agreement protocol
- On the covering number of small symmetric groups and some sporadic simple groups
- Compositions of linear functions and applications to hashing
- Hydra group doubles are not residually finite
- The status of polycyclic group-based cryptography: A survey and open problems
- On irreducible algebraic sets over linearly ordered semilattices
- A nonlinear decomposition attack
