### Abstract

*F*corresponds to a group-like structure called a locality. Given such a locality

*L*, we prove that there is a one-to-one correspondence between the partial normal subgroups of

*L*and the normal subsystems of the fusion system

*F*. As a corollary we obtain that, for any two normal subsystems of a saturated fusion system, there exists a normal subsystem which plays the role of a "product".

Original language | English |
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Publisher | ArXiv |

Publication status | Submitted - 16 Jun 2017 |

### Fingerprint

### Keywords

- math.GR

### Cite this

*Normal subsystems of fusion systems and partial normal subgroups of localities*. ArXiv.

**Normal subsystems of fusion systems and partial normal subgroups of localities.** / Chermak, Andrew; Henke, Ellen.

Research output: Working paper

}

TY - UNPB

T1 - Normal subsystems of fusion systems and partial normal subgroups of localities

AU - Chermak, Andrew

AU - Henke, Ellen

N1 - 26 pages

PY - 2017/6/16

Y1 - 2017/6/16

N2 - Linking systems were introduced to study classifying spaces of fusion systems. Every linking system over a saturated fusion system F corresponds to a group-like structure called a locality. Given such a locality L, we prove that there is a one-to-one correspondence between the partial normal subgroups of L and the normal subsystems of the fusion system F. As a corollary we obtain that, for any two normal subsystems of a saturated fusion system, there exists a normal subsystem which plays the role of a "product".

AB - Linking systems were introduced to study classifying spaces of fusion systems. Every linking system over a saturated fusion system F corresponds to a group-like structure called a locality. Given such a locality L, we prove that there is a one-to-one correspondence between the partial normal subgroups of L and the normal subsystems of the fusion system F. As a corollary we obtain that, for any two normal subsystems of a saturated fusion system, there exists a normal subsystem which plays the role of a "product".

KW - math.GR

M3 - Working paper

BT - Normal subsystems of fusion systems and partial normal subgroups of localities

PB - ArXiv

ER -