linkercosets

Linkercosets are a concept in algebraic combinatorics and group theory describing a refined partition of a group into coset-like blocks connected by a set of elements called linkers. The construction starts with a group G and a subgroup H ≤ G. A linker set L ⊆ G mediates connections between left cosets gH. Two cosets g1H and g2H are linked if there exists a finite sequence of linkers l1, l2, ..., lk ∈ L such that g2H = g1 l1 H and each step moves along a conjugate or translate of the current coset. The equivalence relation generated by this linkage partitions the left cosets into linker coset classes.

If L is closed under taking inverses, the linkage is symmetric; if L is closed under multiplication, it becomes transitive, yielding a genuine partition. Linker cosets often refine the ordinary coset decomposition and can reflect extra symmetry arising from the normalizer of H or from a group action on an auxiliary set.

Applications include symmetry reduction in computational group theory and the study of orbit structures within subgroup lattices. The term is not standard in mainstream algebra and appears chiefly in niche writings; it is sometimes called linkage cosets or linker classes.

References are limited; the concept is presented here as a descriptive, hypothetical construct.