Timeline for Describing the ordinary irreducible characters of a special $p$-group $p^{n+m}$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 20, 2021 at 17:12 | comment | added | Richard Lyons | One interesting case occurs when $P$ admits a group of automorphisms which acts irreducibly on $P/Z(P)$ but trivially on $Z(P)$. Then for every maximal subgroup $M$ of $Z(P)$, $P/M$ is extraspecial (exercise). It follows that every nonlinear ordinary irreducible character of $P$ has degree $p^{m/2}$. | |
| Sep 18, 2021 at 22:15 | comment | added | Derek Holt | Also I don't think the character degrees are a fixed function of $p$, $n$ and $m$. In the case $3^{2+4}$, in some examples there are $36$ of degree $3$ and $4$ of degree $9$, and in others there are $8$ of degree $9$. | |
| Sep 18, 2021 at 22:00 | comment | added | Derek Holt | If $n>1$ then there cannot be any faithful irreducible (complex) representations because the centre is not cyclic. | |
| Sep 18, 2021 at 21:14 | history | edited | LSpice | CC BY-SA 4.0 |
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| S Sep 18, 2021 at 20:26 | review | First questions | |||
| Sep 19, 2021 at 2:17 | |||||
| S Sep 18, 2021 at 20:26 | history | asked | Isaac | CC BY-SA 4.0 |