The Brahmanical ideal of exogamy suggests that individuals should marry following what?

Outside their kin group.

From around c. 1000 BCE onwards, one of the Brahmanical practices was the classification of people, especially Brahmanas, based on their "gotras." Each gotra was named after a Vedic seer, and individuals belonging to the same gotra were considered descendants of that seer. Notably, two significant rules concerning gotras were in place: First, women were expected to relinquish their father's gotra and adopt their husband's gotra after marriage. Second, individuals belonging to the same gotra were forbidden from marrying each other.

To ascertain the prevalence of these rules, historians have examined the names of men and women, which were often derived from gotra names. For instance, powerful ruling lineages like the Satavahanas, who ruled parts of western India and the Deccan from the second century BCE to the second century CE, provide insights through their inscriptions that allow tracing family connections, including marriages. Interestingly, some Satavahana rulers were polygynous, having multiple wives.

A close examination of the names of women who married Satavahana rulers reveals that many retained their father's gotra names (such as Gotama and Vasistha) instead of adopting names derived from their husband's gotra, as prescribed by Brahmanical rules. Furthermore, some of these women belonged to the same gotra, which deviated from the ideal of exogamy (marrying outside the kin group) advocated in Brahmanical texts. Instead, this practice exemplified endogamy, wherein marriages within the kin group, such as cousins marrying each other, were prevalent among several communities in South India. Such endogamous marriages fostered close-knit communities.