Yes, it is permissible but not recommended. Marriage is the practice of the Prophet Muhammad (SAWA) and Ahlul Bayt (AS). Those who deliberately leave marriage are not following the Sunnah of the Prophet(SAWA).
Lady Mariam (AS) did not marry for a valid reason but Lady Fatimah (AS) who is the greatest lady, did marry.
It is Makrouh (disliked) to deliberately abondon marriage.
It is also Makrouh to to live alone at home. Sleeping alone at home is Makrouh. Eating alone is Makrouh as well.