Google has not disclosed which characters are or not allowed in Google Groups emails addresses. The corresponding help article just says the following
Create a group & choose group settings
||Enter an email address for the group. If more than one domain is displayed, select the appropriate domain from the list. Follow these guidelines:
- Email addresses can be up to 63 characters long. This limit doesn't include the domain portion of the address, such as @gmail.com.
Regarding the use of dots in Gmail, they are related to a Gmail feature that, I think will be fair to call innovative and unique, dot aliases. While users can set an email address using dots on Gmail account creation, Gmail automatically sets the name without dots as an alias (let's keep this discussion informal here). Google Groups doesn't support dot aliases. Proof? The Google Groups (for consumers) documentation doesn't mention that aliases are supported.