The Pure opposed Fenrir's Chosen, another group formed by former E88 members, and spent much of their time fighting them. They were somewhat more moderate than the old Empire. While Purity considered herself and her team heroic individuals 
they remained as racist as their progenitor organization.
Following Jack Slash's threat to kill thousand people should Theo Anders not stop him, the Pure left Brockton Bay. Thought they were partially pushed out by the ascendant villain groups there.  They trained Theo and searched for a way to give the boy powers. Thy ultimately ended up abandoning him in Harvard University, Cambridge in an attempt to isolate him and cause a trigger event.
"I won't spoil the conclusion if you're eager to see this through."
This article contains MAJOR SPOILERS relating to
some of the most pivotal parts of Worm. Although all articles contain spoilers, this article will reveal major plot twists and should almost certainly be avoided unless you have finished the story.
↑“Right. It’s okay, it’s understandable, given all we’re trying to handle,” Weld reassured her, “But we can’t miss out on details and updates on the overall situation. The Protectorate have their hands full with the gang wars between Fenrir’s Chosen, Purity’s group and Coil, they’re now dealing with this serial killer or serial killers, and they’re still updating the records. So here’s what we’re going to do, I’ve checked it with Piggot, she agrees. I’m picking up an extra patrol shift, and I’ll be adjusting your patrol shifts down by twenty minutes each, moving them around slightly. With the downtime that creates, we’re going to have meetings like this, every day.” - Excerpt from Sentinel 9.4
↑The Pure – One of two groups that entered play when Empire Eighty-Eight dissolved. Led by Purity, second hand to Kaiser, the Empire’s previous leader. The Pure maintain, or even exaggerate Kaiser’s ‘civilized’ approach. The Pure remain vehement racists and are exceedingly dangerous to those who stand in their way, and have recently left Brockton Bay.---Cast (in depth)
↑“This evidence was assumed using legal methods, of course,” Piggot spoke.
“Of course,” Kid Win grinned in a way that left no doubt for anyone present that he was lying through his teeth. “We believe this unknown party is Coil. There’s no other criminals in town that would really do this. Fenrir’s Chosen aren’t that subtle, and they’re too racist to work with Chariot. Purity’s group is, again, too racist. The Undersiders aren’t well-funded enough. It doesn’t fit the Travelers’ MO.”--Excerpt from Sentinel 9.5
↑ 6.06.16.2“And this second group, The Pure, is the second offshoot of that Aryan group, I take it?”
“Small but powerful. Their leader, Purity, is a Blaster 8 and Mover 4.”
“Yeah, there’s a Breaker 9, a Shifter 8 with Stranger 3 and a Master 6 in that group? I buy that they’re powerful.”
“Their leader has made overtures to us, offering cooperation in helping us regain control of the city. We have refused her for the time being. If she approaches you, you are in no way, shape or form permitted to agree to any deals.”---Excerpt from Sentinel 9.1
↑“What’s important is it won’t be in the next little while. If they intend to send someone like Eidolon or Alexandria here, even, it won’t be anytime soon. So I can give you the official announcement. We won. Job complete. The Pure have hauled ass out of town, Faultline’s apparently decided it’s safer to be out of the city, and you’ve humiliated the heroes enough that they can’t honestly contest your claim. There’s nobody left.”
“The city is ours. And here’s the thing. Order from the one in charge,” Lisa paused, and her meaning was clear. An order from Coil. “You’re done. Good job. Your final order for the time being is to take a few days off. No costumed tomfoolery. Go back to your territories, make sure things are okay, but no getting into fights. If I see you out in costume, you’re fired. Hell, I’ll shoot you.”-- Excerpt from Monarch 16.5