# Questions tagged [schur-multipliers]

The tag has no usage guidance.

23 questions
Filter by
Sorted by
Tagged with
310 views

187 views

### In which books we can find structure information for finite simple groups and their Schur covering groups?

In which books we can find representations or character tables, Sylow 2-subgroups and conjugacy classes for finite simple groups and their Schur covering groups and properties for Schur multiplier of ...
284 views

### Is $1\neq a\in Z(2.E_7(q))\cong Z_2$ a square element in $2.E_7(q)$?

When $q$ is a power of some odd prime, is $1\neq a\in Z(2.E_7(q))\cong Z_2$ a square element in $2.E_7(q)$? A Lie algebra is a vector space $L$ over a field $K$ on which a product operation $[xy]$ is ...
239 views

Let $G$ be a finite group and $H$ a normal subgroup of $G$. I recently stumbled upon the following identity for the Schur multiplier of $G/H$: $$\operatorname{H}_2(G/H,\mathbb{Z}) \cong \frac{\... 0answers 138 views ### Examples for Bogomolov multiplier of finite group Take G to be a finite group. The projective representations of G are classified by the group cohomology H^2(G,U(1)). Here G has a trivial action on U(1). We focus on the restriction map H^... 1answer 230 views ### Schur covers of affine 2-transitive groups I am interested in Schur covers of minimal 2-transitive groups. A theorem of Burnside gives that every finite 2-transitive group is either almost simple or affine. In the time since, these groups have ... 1answer 122 views ### Convergence of sequence of images of Schur multipliers Let \eta be a continuous bounded function on (0, \infty)^{2} so that \eta(0,0)=1. Let A be a bounded operator on \ell^{2}(\mathbb{Z}_{\geq 0})=\ell^{2} (by bounded operator I will always ... 1answer 98 views ### Kernel of a double cover of group as stem extension A stem extension of a group X is a group G with a subgroup N contained in G' \cap Z(G) such that G/N is isomorphic to X, so that we have a short exact sequence 1 \to N \to G \to X \to 1. ... 0answers 115 views ### When is the restriction map res:H^2(G,U(1))\to H^2(Z_p\times Z_p,U(1)) not the zero map? Consider G to be a finite group with non-trivial Schur Multipler H^2(G,U(1)), where G acts trivially on the circle group U(1). By Example of a Schur-nontrivial group with no abelian subgroup ... 1answer 146 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 ... 0answers 164 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 ... 1answer 73 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 \... 0answers 166 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 ... 1answer 366 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 ... 1answer 294 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/... 0answers 95 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 [... 2answers 613 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 (... 0answers 134 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 $C_0(G)\otimes C_b(G)$)
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 ...