The office, rank, or status of being a grenadier, or the body of grenadiers as a collective group.
From grenadier + -ship (Old English suffix denoting status, office, or condition), like 'citizenship' or 'leadership'.
Grenadiership represented prestige in ways modern military ranks don't—it was simultaneously a job, a brotherhood, and a visible marker of elite status that affected every aspect of a soldier's career.
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