Is it permissible for a muslim woman to become a gynecologist1?
- Gynecology:the branch of physiology and medicine that deals with the functions and diseases specific to women and girls, esp. those affecting the reproductive system. Ref: The OED
The short answer is yes. As @Abdullah mentioned, it's even encouraged to take up such positions. These kind of jobs avoid the chance for women to uncover their Awara's(in this case their private parts) in front of a male doctor. Working in such field is considered Fard Kefaya(where everyone is accountable in the community and if one person fulfills it, the responsibility is lifted from the whole community).
The only condition for this is that the job doesn't neglect your duties toward your home, children and husband; and you have your husband or guardian permission– because these are considered Fard ‘ayn and take precedence over Fard Kefaayee. For more information please follow the link enfolded in the text above.