Praise be to Allaah.
One of the ways in which Islam protects women is that it requires a woman to travel with a mahram, to protect her from those who have bad intentions and to help her, because of her weakness, in facing the arduous trials of travelling. A woman is not permitted to travel without a mahram because of the hadeeth narrated by Ibn ‘Abbaas (may Allaah be pleased with him), who reported that the Prophet (peace and blessings of Allaah be upon him) said: “A woman should absolutely not travel unless she has a mahram with her.” A man stood up and said, “O Messenger of Allaah, I have enlisted in such-and-such a military campaign, and my wife has set out for Hajj.” He said, “Go and do Hajj with your wife.” (al-Bukhaari, al-Fath, 3006).
What indicates that a mahram is obligatory is the fact that the Prophet (peace and blessings of Allaah be upon him) commanded this man to give up the idea of jihaad (on this occasion), even though he had enlisted for a campaign and his wife was travelling for the purpose of worship, not for some frivolous or suspicious reason. In spite of all this, he told him to go and do Hajj with his wife.
The ulamaa’ have listed five conditions for a person to be considered a mahram. He should be male, Muslim, adult, and of sound mind, and he should be a relative to whom marriage is permanently forbidden, such as a father, brother, paternal uncle, maternal uncle, father in law, mother’s husband or brother through radaa’ah (breastfeeding), etc. (as opposed to relatives to whom marriage is temporarily forbidden, such as a sister’s husband, paternal aunt’s husband, maternal aunt’s husband).On this basis, the husband’s brother and the son of a paternal or maternal uncle are not mahrams, so it is not permitted for her to travel with them. And Allaah knows best