reference request – On a result by Rubin on elementary equivalence of homeomorphism groups and homeomorphisms of the underlying spaces

In the known paper On the reconstruction of topological spaces from their group of homeomorphisms by Matatyahu Rubin several deep reconstruction theorems of the form “if $X$ and $Y$ are topological spaces in a broad class of spaces $K$ and there is an isomorphism between $mathrm{Homeo}(X)$ and $mathrm{Homeo}(Y)$, then $X$ and $Y$ are homeomorphic” are proved. Moreover the following result is claimed

Assume $V=L$. If $X$ and $Y$ are second countable connected Euclidean manifolds and $mathrm{Homeo}(X)$ is elementary equivalent to $mathrm{Homeo}(Y)$, then $X$ and $Y$ are homeomorphic.

to appear in Second countable connected manifolds with elementarily equivalent homeomorphism groups are homeomorphic in the constructible universe. Unfortunately I cannot find any information on a paper with this title online. Has a proof of this theorem been published by Rubin? What is known about this result in $mathsf{ZFC}$ without extra set theoretic assumptions?

Can we use Power automate to automate creating new users inside Office 365 and assign them list of groups

I received a request to create a power automate Flow for HR managers as follow:-

  • The HR Manager will add the user name inside a SharePoint list >> then the flow will automatically start

  • The flow will import all the email groups from Azure Ad and show them to the user.

  • The flow will allow the user to chose what groups they want the user to be part of

  • The flow will allow the user to choose the user work location from a list

  • The flow will allow the user to choose the user role

  • The flow will allow the user to choose the user manager

  • Then the flow will create the user automatically on the local AD

Can we create such as workflow inside power automate ?


notebooks – Locking cell groups

Imagine I have a notebook divided into multiple groups of code cells which are set as initialization groups. I then have a single cell which evaluates a function program() that yields an interactive tool (for example via Manipulate) which internal functions are defined in the initialization groups. Something like

enter image description here

If these groups are collapsed, is it possible to lock them so that when I share the notebook the code in these groups remains hidden and private and the only accessible cell is the one to run the program?

Which local groups beside Local Administrator allow elevating privileges to administrator on Windows 10?

Which local groups beside Local Administrator allow elevating privileges to administrator on Windows 10?

To ensure that local users cannot elevate their privileges to administrator solely by using their local group memberships, I want to audit local group memberships (e.g. Local Administrator.)

Are there other local groups that can be used to easily elevate privileges to administrator? If so, how?

drag n drop – Best UI pattern for letting a user assign items to groups

Problem: the user has a list of about 5-20 uncategorised items and needs to categorize them into 2-4 groups. The tricky part is that the same item can be placed into more than one group (this is an edge case but needs to be supported).

From what I can see there are two design patterns that apply:

Basically user is provided with a list of drag-able items which he/she can then bucket inot groups

The main issue with this pattern is that because the same item can be placed into more than one group it means that it’s not really a ‘move’ interaction, the item has to stay in the uncategorised list in order for the user to be able to also place it into another category. Another consequence of this is that the uncategorised list never shrinks so it’s not immediately clear which of the items in it have been grouped and which remain unassigned

Here is a possible design that tries to handle the above issues. Items which have been assigned to groups appear darker. Also I use color (coloured dot corresponding to the group label color) to help the user see which group(s) the item has been put under.

enter image description here

Checkbox table:
A table-style UI where each item can be assigned to a group by checking the checkbox for that group’s column. Checkboxes rather than radio buttons are used because of the multiple group assignment per item requirement. Here is an example:

enter image description here

The main disadvantage I see with this UI is that it’s not immediately easy to see what items belong to a given group. Also it’s a bit more clumsy to move items between groups once assigned (2 step action: user has to uncheck one checkbox and check another one). This can be remedied by providing a separate listing of the items in each group beside the assignment table UI. This list can either be non-interactive or support drag-n-drop for moving items between groups. Example:

enter image description here

To be honest I’m not completely satisfied with either solution. I’m wondering if anyone has any better ideas or improvements to this design?

8 – Nested conditions groups in views filter plugin

I need to nest some “where Groups” on a QueryPluginBase query, but I can only nest first depth group to the main “where” using setWhereGroup. I need to add groups into another groups but there isn’t a function to do it because setWhereGroup let you add a new OR/AND group but I can’t set the parent group ID I’d like to nest. For example, I’d need:

((Condition1 OR Condition2) AND ( (Condition3 OR Condicion4) AND (Condition5 OR Condition6) )) OR (Condition7)

This is my custom views filter plugin:

namespace Drupalmy_modulePluginviewsfilter;

use DrupalviewsPluginviewsfilterFilterPluginBase;
use DrupalviewsPluginviewsdisplayDisplayPluginBase;
use DrupalviewsViewExecutable;

 * My custom filter
 * @ingroup views_filter_handlers
 * @ViewsFilter("my_custom_filter") 
class MyCustomFilter extends FilterPluginBase {

     * {@inheritdoc}
    public function init(ViewExecutable $view, DisplayPluginBase $display, array &$options = NULL) {
        parent::init($view, $display, $options);
        $this->valueTitle = t('Filtro agendas usuario');

    public function query() {
      $this->query->setWhereGroup('OR', '90');
      $user_org = $user->field_usr_org;
      foreach ($user_org as $org) {
         $this->query->addWhere('90', 'mytable.myfieldid', $org->target_id, '=');

      $this->query->setWhereGroup('OR', '91');
} theory – on the group generated by transitive permutation groups and diagonal groups

Let $T$ be a transitive permutation group in $S_n$, embedded in $GL_n(F)$ as permutation matrices. Let $D$ be the group of diagonal matrices in $GL_n(F)$. Let $G$ be the group generated by $T$ and $D$. That is, $G$ is a subgroup of the monomial group in $GL_n(F)$.

Question: is $G$ irreducible as a matrix group?

Probably this is a very basic question, but I cannot figure it out or find a reference…

Thank you for your help!

availability groups – Remove 2 node Always on setup from SQL Server and failover cluster

We are using 2 node Always-on Availability Group, But Service provider don’t support AOAG. So we need to remove one node from Always-on. How can we convert the primary replica to Standalone instance.

If we stop the cluster roles are we facing any problem.

encryption – Diffie-Helam groups with vsftpd

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.

rt.representation theory – Irreducible representations of product of profinite groups

It is a standard fact in the representation theory of finite groups that for $G,H$ finite groups, all of the irreducible representations of $G times H$ are the external tensor product of irreps of $G$ and $H$. Today I was talking to a friend about profinite groups and it got me thinking: “Is (some version of) this result still true?” The fact that so many results from the finite case carry over makes me think that this could be true, but I have no idea how to go about proving it. The standard proof for finite groups uses a counting argument to show that they are all of this form, so certainly some higher-level techniques will be required.

Since we’re considering profinite groups, we will definitely want to restrict ourselves to continuous representations on topological vector spaces. If the statement is not true in this generality, are there adjectives we can add that make it true? What if our representations are unitary, or the profinite groups are (topologically) finitely-generated? Any results, no matter the number of hypotheses, would be of interest to me.