## Fusion systems on small $p$-groups

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- by David A. Craven and Adam Glesser PDF
- Trans. Amer. Math. Soc.
**364**(2012), 5945-5967 Request permission

## Abstract:

In this article we study several classes of ‘small’ $2$-groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic $p$-groups for all primes $p$. We consider Suzuki $2$-groups, and classify all center-free saturated fusion systems on $2$-groups of $2$-rank $2$. We end by classifying all possible $\mathcal {F}$-centric, $\mathcal {F}$-radical subgroups in saturated fusion systems on $2$-groups of $2$-rank $2$.## References

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## Additional Information

**David A. Craven**- Affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
- MR Author ID: 833948
- Email: d.a.craven@bham.ac.uk
**Adam Glesser**- Affiliation: Department of Mathematics, California State University Fullerton, Fullerton, California 92834
- Received by editor(s): July 9, 2010
- Received by editor(s) in revised form: February 25, 2011
- Published electronically: May 24, 2012
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**364**(2012), 5945-5967 - MSC (2010): Primary 20D20; Secondary 20D45
- DOI: https://doi.org/10.1090/S0002-9947-2012-05580-2
- MathSciNet review: 2946938