Final answer:
A one-male multi-female social group in primates is known as a polygynous group. Females form the core of these groups, often characterized by related females and a transient male, where both sexes are engaged in complex social behaviors involving cooperation and competition.
Step-by-step explanation:
The social group in primates that comprises one adult male, several adult females, and their offspring is commonly referred to as a one-male multi-female group, or a polygynous group. This structure is often seen in species like gorillas, where the male is typically the dominant individual in the group maintaining relationships with multiple females who are central to the group's social life. In the primate hierarchy and social structure, the role of females is significant; they provide care to their young and solidify the social bonds within the group. While primates exhibit various social structures, such as mated pairs or larger multi-male multi-female communities, the one-male multi-female dynamic is notable for its relative stability and the protective role the male may play in the group.
In such groups, the females are often related and form the core of the social structure, with males typically being transient. This female-centric aspect of the society is essential as females invest heavily in offspring, influencing the dynamics of cooperation and competition within the group. Despite this, both males and females are engaged in complex social strategies for accessing resources and mates, indicating the multifaceted nature of primate social organization.