Questions tagged [schur-multipliers]

The tag has no usage guidance.

9 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
6 votes
0 answers
206 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^...
Chao-Ming Jian's user avatar
4 votes
0 answers
129 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 ...
David Stephen's user avatar
4 votes
0 answers
175 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 ...
Alin Galatan's user avatar
2 votes
0 answers
64 views

Is there a method to find the order of a lift of an element of order 2 to the Schur cover?

Let $G$ be a finite non-abelian simple group, $M.G$ the Schur covering group of $G$. Is there a method to find the order of a preimage of an element of order 2 in the natural homomorphism $\pi: M.G\...
Yi Wang's user avatar
  • 261
1 vote
0 answers
61 views

Reference request for finite simple exceptional group of lie type $E_7(q)$ and its Schur covering group $2.E_7(q)$?

Does anyone have the paper named 'Génerateurs, relations et revêtements de groupes algébriques' written by Robert Steinberg in 1962, or any other reference for simple groups of Lie type $E_7(q)$ and ...
Yi Wang's user avatar
  • 261
1 vote
0 answers
227 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 ...
Steve's user avatar
  • 255
1 vote
0 answers
105 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 [...
Steve's user avatar
  • 255
0 votes
0 answers
78 views

What do Sylow 2-subgroups look like for Schur covering groups of finite simple groups?

What do Sylow 2-subgroups look like for Schur covering groups of finite simple groups? Are there any references in which we can find the stucture of Sylow 2-subgroups of Schur covering groups of ...
Yi Wang's user avatar
  • 261
0 votes
0 answers
145 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 $C_0(G)\otimes C_b(G)$)
zzzz's user avatar
  • 1