are the women a part of this league?
Yes,  Marguerite Norris the first woman NHL executive was first woman to have her name engraved on the Stanley Cup.
National Hockey League
 In 1992, Manon Rheaume became the first woman to play a game in any of the major professional North American sports leagues, as a goaltender for the Tampa Bay Lightning in an NHL pre-season game against the St. Louis Blues, stopping seven of nine shots. 
which game is played in stanley cup? Hockey who is its organizer? UNANSWERABLE which competition did it organize? ice hockey is anything engraved on its trophy? It is engraved with the names of the winning players, coaches, management, and club staff. which hockey league is associated with it? National Hockey League
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National Hockey League [SEP] Women in the NHL
From 1952 to 1955, Marguerite Norris served as president of the Detroit Red Wings, the first woman NHL executive and the first woman to have her name engraved on the Stanley Cup. In 1992, Manon Rheaume became the first woman to play a game in any of the major professional North American sports leagues, as a goaltender for the Tampa Bay Lightning in an NHL pre-season game against the St. Louis Blues, stopping seven of nine shots. In 2016, Dawn Braid was hired as the Arizona Coyotes' skating coach, making her the first female full-time coach in the NHL. The first female referees in the NHL were hired in a test-run during the league's preseason prospect tournaments in September 2019.