According to someone's conspicuous impressions (which could be alleged ensuingly).(adverb)
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Use "allegedly" in a sentence
"That's two uses of the term allegedly thus far and we're still at the trail head of the lead sentence!"
"This is about whether any person appointed by that allegedly corrupt governor and I use the term allegedly loosely can serve and be effective in the position, given the circumstances surrounding the appointment."
"The lawsuit concerns some two dozen songs, for which the label allegedly has not paid royalties to artists for their use in compilations and as ringtones."