At the Seventh Level by Suzette Haden Elgin

At the Seventh Level by Suzette Haden Elgin tells the story of Coyote Jones on the recently-civilized planet of Abba. After reluctantly satisfying the Society of Civilized Planets' concessions on its treatment of women, Jacinth, a brilliant female, rose to the highest rank in the planet's strange society. But her success leads to male fury, female envy, and a deviously evil plan that may cost Abba its status.