Who is considered a permanent Mahram (unmarriageable relation) for a woman?

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A permanent Mahram is either her husband or one to whom she is permanently forbidden due to lineage or a permissible cause, such as her father, son, or brother, whether through lineage or fosterage. Evidence for this requirement, particularly regarding travel, is the statement of the Prophet, peace be upon him: 'It is not lawful for a woman who believes in Allah and the Last Day to travel a distance of three days or more except with her father, or her son, or her husband, or a Mahram relation.' This is narrated by Muslim. Furthermore, the husband of a woman's mother is a Mahram to her for Hajj. A man may travel with the mother of his grandfather's slave-woman, and a woman may travel with her foster-brother.