The schur-multipliers tag has no usage guidance.

**0**

votes

**1**answer

51 views

### Example of a Schur-nontrivial group with no abelian subgroup of the form $H\times H$?

A group $G$ is Schur-nontrivial if the Schur multipler $H^2(G,U(1))$ is not the trivial group.
I am trying to find an example of a Schur-nontrivial group which does not contain a subgroup of the form ...

**0**

votes

**0**answers

71 views

### When can a 2-cocycle on a subgroup can be extended?

This question is based on a question when is the restriction $H^2(G,\mathbb{C}^*)\to H^2(K,\mathbb{C}^*)$ surjective?
I am asking this as a new question as I already asked that user but got no ...

**1**

vote

**1**answer

51 views

### How to claculate the $T$-stable subgroup of second cohomology group

Let $G=\langle x,y,z,w \mid [y,x]=w^p=z, x^{p^2}=y^p=z^p=1 \rangle$ be a group, where $[u,v]=u^{-1}v^{-1}uv$, $p$ is a prime and the commutator which do not appear is 1.
Let $N=\langle y,w \rangle \...

**4**

votes

**0**answers

145 views

### Is the Tensor/Exterior square $G\otimes G$ or $G\wedge G$ of infinite p-group also a p-group?

Let $G$ be an infinite countable p-group. Is it true that $G\otimes G$ or $G\wedge G$ are also p-groups? (where G acts on itself by conjugation). For simplicity, you can consider that $G=[G,G]$, and ...

**6**

votes

**1**answer

228 views

### What is the Schur multiplier of the affine linear group AGL(n,q)?

What is the Schur multiplier of the $n$-dimensional affine linear group $\mathrm{AGL}(n,q)$ over the Galois field with $q$ elements?
I am particularly interested in the simple case $n=1$. Computation ...

**1**

vote

**1**answer

215 views

### Two questions on the Schur multiplier of groups of order $p^4$

I tried to find a reference for the computation of the Schur multiplier of groups of order $p^4$.
The case in which $p=2$ is well known, see e.g. Table 1 at http://pages.bangor.ac.uk/~mas010/pdffiles/...

**1**

vote

**0**answers

78 views

### Homology and Exterior Square

Let $G$ be a finite group and $G \wedge G$ denote the exterior square of $G$. It is well known that the second integral homology $H_2(G,\mathbb{Z})$ is the kernel of homomorphism $x \wedge y \mapsto [...

**11**

votes

**2**answers

536 views

### How hard (P, NP, NP-hard) is it to compute Schur norms of matrices (as multipliers)?

Given a matrix $A\in M_n(\mathbb{C})$, I will denote by $||A||_\infty$ the operator norm of $A$, as seen acting on the Hilbert space $\mathbb{C}^n$. This makes $M_n(\mathbb{C})$ into a Banach space (...

**0**

votes

**0**answers

124 views

### A question about multiplier algebra of $C_0(G)\otimes C_b(G)$ for a locally compact group $G$

Let $G$ be locally compact group. How we can show that
$$
M(C_0(G)\otimes C_b(G))=C_b(G,C_b(G)).
$$
($M(C_0(G)\otimes C_b(G))$ is the multiplier algebra of $C_0(G)\otimes C_b(G)$)

**29**

votes

**2**answers

2k views

### Why are Schur multipliers of finite simple groups so small?

Given a finite simple group $G$, we can consider the quasisimple extensions $\tilde G$ of $G$, that is to say central extensions which remain perfect. Some basic group cohomology (based on the ...

**10**

votes

**1**answer

391 views

### Schur multipliers over non-algebraically closed ground fields?

Recently some arithmetic dynamicists came to town, bringing with them some interesting problems in arithmetic geometry.
I started thinking a bit about one of their problems, and it got me wondering ...