Final answer:
A primate social group with one reproductively active female, several adult males, and offspring is known as a polyandrous system. This type of arrangement is among the diverse social structures observed in primates, though less common compared to other types such as monogamous pairs or polygynous groups.
Step-by-step explanation:
The social group in primates that includes one reproductively active female, several adult males, and their offspring refer to a polyandrous social structure. This is not the most common social arrangement among primates, but can occasionally be observed. It contrasts with other social structures such as the multi-male/multi-female groups, monogamous pairs, or one-male with multi-female groups (polygynous). Primate social organization is complex and varies widely across species. For example, bonobos have a matriarchal society where sexual behavior is used as a social tool, and chimpanzees tend to have a patriarchal and more aggressive social hierarchy. In gorilla groups, typically there is one silverback male that mates with the females, and the females tend to leave the group when ready to mate. Understanding primate biology and behavior helps scientists comprehend the evolution of complex social relationships and cognitive abilities that are significant characteristics of human development. It concludes that neither male nor female primates can be seen as passive or dominant by default, and both are essential and active contributors to their social environments.