Questions tagged [p-groups]
The p-groups tag has no usage guidance.
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Representation theory of p-groups in particular upper tringular matrices over F_p
Finite p-groups - have p^n elements by definition. According to WP there is rich structure theory.
Question: How far is representation theory of p-groups is understood?
In case this question is too ...
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p-groups as rational points of unipotent groups
Is it true that every finite p-group can be realized as the group of rational points over $\mathbb{F_p}$ of some connected unipotent algebraic group defined over $\mathbb{F_p}$? For abelian p-groups, ...
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Variety of nilpotent Lie algebras or $p$-groups
Here's a couple of analogous questions, one in terms of finite-dimensional complex Lie algebras and one in terms of finite $p$-groups; I'd be interested in an answer to either:
1) Let $\mathcal{L}$ ...
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How can I get my hands on McKay's "Finite p-groups" lecture notes?
How can we find Susan McKay's "Finite $p$-groups" lecture notes?
The notes I'm talking about are these.
I emailed Peter Cameron, but he has since moved to a different university, and has no ...
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Is there a subgroup of a non-abelian $p$-group $G$ with a large nilpotency class?
Let $G$ be a non-abelian $p$-group ($p\ne2$). Does there exist a group $H\subset G$ such that both 1, 2 are satisfied?
$|H| = |G|/p$.
$c(H)\geq c(G) - 1$.
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A class 3 group of order 243
Let G be a group of order $243=3^5$. We denote by $(G_i)$ its lower central series and assume that $G$ has class $3$ and that $|G:G_2|=|G_3|=9$. We assume moreover that the cubing map factors as a (...
user76083
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Finite p-groups and their fibered products
Is every finite $p$-group an epimorphic image of a fibered product of two finite $p$-groups which can be generated by $2$ elements?
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Union of conjugates in p-groups
Fix a prime number $p$. Is there a sequence $\{a_k\}_{k \in \mathbb{N}}$ of real numbers with $$\lim_{k \to \infty} a_k = 0$$
such that for any finite $p$-group $G$, and any subgroup $H \leq G$ with ...
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