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- 01:16, 9 January 2026 Multi-invariance equals strongly intersection-closed in Noetherian group (hist | edit) [6,141 bytes] Vipul (talk | contribs) (Created page with "==Statement== Let <math>p</math> be a subgroup property and <math>G</math> be a Noetherian group. Then, the following are equivalent: * <math>p</math> is a multi-invariance property when restricted to <math>G</math>, there is a collection <math>\{ F_n \}_{n \in \mathbb{N}}</math> of <math>n<math>-ary functions on <math>G</math> such that the subgroups satisfying <math>p</math> are precisely the ones invariant under all these functions. * <math>p</math> is a...")
- 01:05, 9 January 2026 Strongly intersection-closed not implies union-closed (hist | edit) [2,913 bytes] Vipul (talk | contribs) (Created page with "{{subgroup metaproperty non-implication| stronger = strongly intersection-closed subgroup property| weaker = union-closed subgroup property}} ==Statement== ===General statement=== It is possible to have a strongly intersection-closed subgroup property <math>p</math> (a subgroup property closed under arbitrary intersections, including the empty intersection, and therefore true for every group as a subgroup of itself) that is not a union-closed subgroup proper...")
- 00:42, 9 January 2026 Strongly intersection-closed not implies invariance (hist | edit) [1,130 bytes] Vipul (talk | contribs) (Created page with "{{subgroup metaproperty non-implication| stronger = strongly intersection-closed subgroup property| weaker = invariance property}} ==Statement== ===General statement=== It is possible to have a strongly intersection-closed subgroup property <math>p</math> (a subgroup property closed under arbitrary intersections, including the empty intersection, and therefore true for every group as a subgroup of itself) that is not an invariance property. ===Statement w...")