Can my users have a single sign on experience when using Office 365? I.e. not have to enter a username and password for SharePoint when in the office?

Yes, but only on the Enterprise plans E1-3, by configuring ADFS integration.

SharePoint Blogs

In 2009 I went to Microsoft’s developer conference, TechEd. This was the same year that the first iPhone was released, and the mobility movement was...
If you’re a regular SharePoint user, you’ve probably wondered if your workplace could do more to organise and manage documents in the right way. Is...
By now you’ll understand the value of investing in a digital workplace. We all want to make work easier and more effective: improve productivity,...