Charles Eaton: Created page with "{{blockbox |title = M(16,10,1) - $k(C_4 \times C_2 \times C_2)$ |image = |representative = $k(C_4 \times C_2 \times C_2)$ |defect = $C_4 \times C..."$

2018-12-04T08:41:19Z

Created page with "{{blockbox |title = M(16,10,1) - <math>k(C_4 \times C_2 \times C_2)</math> |image = |representative = <math>k(C_4 \times C_2 \times C_2)</math> |defect = <math>C_4 \times C..."

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{{blockbox
|title = M(16,10,1) - <math>k(C_4 \times C_2 \times C_2)</math>
|image =
|representative = <math>k(C_4 \times C_2 \times C_2)</math>
|defect = <math>C_4 \times C_2 \times C_2</math>
|inertialquotients = <math>1</math>
|k(B) = 16
|l(B) = 1
|k-morita-frob = 1
|Pic-k=
|cartan = <math>\left( \begin{array}{c}
16 \\
\end{array} \right)</math>
|defect-morita-inv? = Yes
|inertial-morita-inv? = Yes
|O-morita? = Yes
|O-morita = <math>\mathcal{O} (C_4 \times C_2 \times C_2)</math>
|decomp = <math>\left( \begin{array}{c}
1 \\
1 \\
\vdots \\
1 \\
\end{array}\right)</math>
|O-morita-frob = 1
|Pic-O = <math>\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)</math>
|PIgroup =
|source? = No
|sourcereps =
|k-derived-known? = Yes
|k-derived = Forms a derived equivalence class
|O-derived-known? = Yes
|coveringblocks = M(16,10,1), [[M(16,10,3)]] (complete)
|coveredblocks = M(16,10,1), [[M(16,10,3)]]<ref>For example consider the block of <math>C_4 \times PSL_3(7)</math> covering block number 2 of <math>PSL_3(7)</math> in the labelling used in [http://www.math.rwth-aachen.de/~MOC/decomposition/tex/L3(7)/]. We have <math>C_4 \times PSL_3(7) \triangleleft C_4 \times PGL_3(7)</math>.</ref> (complete)
|pcoveringblocks =
}}

These are [[Nilpotent blocks|nilpotent blocks]].

== Basic algebra ==

'''Quiver:''' a:<1,1>, b:<1,1>, c:<1,1>

'''Relations w.r.t. <math>k</math>:''' <math>a^4=b^2=c^2=0</math>, <math>ab+ba=ac+ca=bc+cb=0</math>

== Projective indecomposable modules ==



== Irreducible characters ==

All irreducible characters have height zero.

[[C4xC2xC2|Back to <math>C_4 \times C_2 \times C_2</math>]]

== Notes ==

<references />

M(16,10,1) - Revision history

Charles Eaton: Created page with "{{blockbox |title = M(16,10,1) - k(C_4 \times C_2 \times C_2) |image = |representative = k(C_4 \times C_2 \times C_2) |defect = C_4 \times C..."

Charles Eaton: Created page with "{{blockbox |title = M(16,10,1) - $k(C_4 \times C_2 \times C_2)$ |image = |representative = $k(C_4 \times C_2 \times C_2)$ |defect = $C_4 \times C..."$