# Difference between revisions of "C4"

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== Blocks with defect group <math>C_4</math> == | == Blocks with defect group <math>C_4</math> == | ||

− | These are blocks with | + | These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]]. |

There is a unique <math>\mathcal{O}</math>-Morita equivalence class. | There is a unique <math>\mathcal{O}</math>-Morita equivalence class. | ||

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! scope="col"| Class | ! scope="col"| Class | ||

! scope="col"| Representative | ! scope="col"| Representative | ||

+ | ! scope="col"| # lifts / <math>\mathcal{O}</math> | ||

! scope="col"| <math>k(B)</math> | ! scope="col"| <math>k(B)</math> | ||

! scope="col"| <math>l(B)</math> | ! scope="col"| <math>l(B)</math> | ||

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|- | |- | ||

− | |[[M(4,1,1)]] || <math>kC_4</math> ||4 ||1 ||<math>1</math> ||<math>D_8</math> || ||1 ||1 || [[Image:M(4,1,1)tree.png|45px]] | + | |[[M(4,1,1)]] || <math>kC_4</math> || 1 ||4 ||1 ||<math>1</math> ||<math>D_8</math> || <math>(k \times k):k^*</math> ||1 ||1 || [[Image:M(4,1,1)tree.png|45px]] |

|} | |} | ||

+ | |||

+ | [[Category:Cyclic p-group]] | ||

+ | [[Category: p-group]] |

## Latest revision as of 11:18, 22 November 2018

## Blocks with defect group [math]C_4[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees.

There is a unique [math]\mathcal{O}[/math]-Morita equivalence class.

Class | Representative | # lifts / [math]\mathcal{O}[/math] | [math]k(B)[/math] | [math]l(B)[/math] | Inertial quotients | [math]{\rm Pic}_\mathcal{O}(B)[/math] | [math]{\rm Pic}_k(B)[/math] | [math]{\rm mf_\mathcal{O}(B)}[/math] | [math]{\rm mf_k(B)}[/math] | Notes |
---|---|---|---|---|---|---|---|---|---|---|

M(4,1,1) | [math]kC_4[/math] | 1 | 4 | 1 | [math]1[/math] | [math]D_8[/math] | [math](k \times k):k^*[/math] | 1 | 1 | 45px |