The phrase "allowed to push a" is correct and usable in written English.
It can be used in contexts where permission is granted to perform an action, typically in a directive or instructional setting.
Example: "In this game, players are only allowed to push a button once per turn."
Alternatives: "permitted to push a" or "authorized to push a".
When rats are allowed to push a lever in exchange for a mild current that produces a "high" in the "pleasure centers," they will press the lever up to 7,000 times per hour.
Usually you're not allowed to push a goalie into the net.
The oft-cited danger in every Dapper Laughs being allowed to push a laddish agenda on TV still is that his antics will be parroted and copied by a generation of lads who think that street harassment is hilarious.
Joe Hockey has used the fact that he was not allowed to push two tables together at a pizza restaurant as an illustration of why the government needs to act on cutting red tape.
As part of the promotion, CoverGirl allowed consumers to download the "Umbrella" video on its Web site and put displays in stores near its Fruit Spritzers product that allowed consumers to push a button to hear the song.
This allowed extremists to push "a relatively close-knit group" focused on overthrowing Gaddafi into joining the pan-Islamist terror network.
The museum has interactive video displays that allowed you to push a button, hear a story and watch a brief portion of an interview.
One reason is that Hahn's friendly mien, just this side of Mister Rogers, allowed him to push a mean-spirited message in his television advertising and direct-mail campaign.
"The background app refresh allows us to push a user's ticket to their device in real time.
Inertia and friction will not allow one to push a 300-pounder out of the way any more than they would on earth.
The Mayday feature is free of charge - allowing users to push a button to be put in contact with Amazon customers support (either video or audio depending on your connection quality) who you can then ask for help.
