The fields that include the support groups on a ticket are referred as an assignment menu. Here are the applications that make use of this functionality: Incident, Problem, Change, Release,  Asset, Service Request, Knowledge, Configuration, Task and Activity.

When a support group is created for a company, it is available for resolving the company’s tickets.  Configuring valid support groups for a company is necessary in the following scenarios:

- A company might have multiple support groups but all the support groups may not be relevant to a ticket. Having an irrelevant support group in the assignment menu might lead to confusion or incorrect assignment.

The Support Group Assignment Configuration form allows configuration for a valid support groups for a company, which can be used to resolve tickets. 

Use case: 
Allow users in Group B to assign tickets to Group A or Group B,

1. Log into Remedy as an Administrator. On the application fly out menu select Administration Console > Application Administration Console > Custom Configuration tab > Foundation > Advanced Options > Support Group Assignment Configuration to display the Support Group Assignment Configuration form. 
2. Select Company A in Support Company and Company B in Service company Assignment Support Groups.
3. Move  Company A to Company B (left to right). First screen capture below example
4. Log out of mid tier. Log into Remedy as a user in Group B and test the results that both groups are available for assignment. Second screen shot below example






For further detailed document go to the following link
 https://docs.bmc.com/docs/itsm2002/support-group-configuration-for-assignments-909627911.html