This is the 15003rd most frequent Russian word.
подстрекаемые
"Incited" or "provoked."
Here, 'подстрекаемые' means 'being encouraged' or 'instigated by', reflecting their friends' influence.
Подстрекаемые своими друзьями, они начали протест.
Encouraged by their friends, they started a protest.
In this case, 'подстрекаемые' suggests being incited or driven towards unethical behavior.
Подстрекаемые к злоупотреблению доверием, они нарушили закон.
Incited to abuse trust, they broke the law.
Here, 'подстрекаемые' refers to being driven or influenced negatively by rumors.