Every infinite group is index-unstable, with a general criterion for index stability in countable groups and exact subindices computed for notable integer sequences.
Kabenyuk, Factors in infinite groups, arXiv:2602.22876v1 [math.GR], (2026)
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Subindices and subfactors of infinite groups and numbers
Every infinite group is index-unstable, with a general criterion for index stability in countable groups and exact subindices computed for notable integer sequences.