Equation 677 Database

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Size 35

274 isomorphism classes.

magma e6571cef of size 35 magma ab7b41b2 of size 35 magma 1f6a47f5 of size 35 magma 5452d53e of size 35 magma 998f8dec of size 35 magma a297e0d6 of size 35 magma 7c7b4a5d of size 35 magma 543c406d of size 35 magma 6c5f4bc9 of size 35 magma 99d8d8c7 of size 35 magma baf57268 of size 35 magma c689a91b of size 35 magma d5b73a25 of size 35 magma 26eaf655 of size 35 magma 5b34fd3d of size 35 magma 9eb5f84c of size 35 magma 4d5e1d7c of size 35 magma 7ce654d3 of size 35 magma 23b1fa43 of size 35 magma 79fcb03c of size 35 magma 50a43b55 of size 35 magma b3b6c29b of size 35 magma 26534c69 of size 35 magma 0b3769f7 of size 35 magma 90d603a5 of size 35 magma ce3fab54 of size 35 magma a9a63e11 of size 35 magma 4ad1a74f of size 35 magma ed4c392b of size 35 magma 113fd524 of size 35 magma 595a4967 of size 35 magma b210a439 of size 35 magma 6468e032 of size 35 magma 0656c290 of size 35 magma b0301159 of size 35 magma 24cee56b of size 35 magma a564691e of size 35 magma 49717cf2 of size 35 magma cb11bd7e of size 35 magma acb7814d of size 35 magma 31a24829 of size 35 magma e35f3c32 of size 35 magma fbd288b2 of size 35 magma 33e103cf of size 35 magma 0c74fd6b of size 35 magma 333976bd of size 35 magma c5f7604b of size 35 magma 2a3822f3 of size 35 magma b8a90deb of size 35 magma 4e316fd7 of size 35 magma 536f91ff of size 35 magma b8ad53af of size 35 magma b84e2661 of size 35 magma 3af77f90 of size 35 magma 61e73e51 of size 35 magma a2e5ecf9 of size 35 magma 08bad707 of size 35 magma a6cd24cd of size 35 magma 498c8d09 of size 35 magma 15e63375 of size 35 magma d23171e2 of size 35 magma 49011aa8 of size 35 magma e6e4d43c of size 35 magma 13e3d9f8 of size 35 magma 96a7fb06 of size 35 magma 706cd453 of size 35 magma 48d89f3f of size 35 magma 5904924b of size 35 magma 7c9866ea of size 35 magma 8d7baed8 of size 35 magma f055d58a of size 35 magma b3327ca9 of size 35 magma 16810bf9 of size 35 magma 27472c9f of size 35 magma 1c244e44 of size 35 magma aaf14997 of size 35 magma 776d0d16 of size 35 magma 331b6db6 of size 35 magma 34046e4a of size 35 magma c5994777 of size 35 magma 111c3ec3 of size 35 magma 0d1a6245 of size 35 magma 4e462f24 of size 35 magma 1c255de8 of size 35 magma 13faee46 of size 35 magma 60549d45 of size 35 magma 4e1438c1 of size 35 magma ba44545e of size 35 magma 50afb0a9 of size 35 magma 61a5cecf of size 35 magma fe238305 of size 35 magma 00b0a9a7 of size 35 magma 33082022 of size 35 magma ff51c433 of size 35 magma 535067a5 of size 35 magma 16507aa5 of size 35 magma 56edd407 of size 35 magma aecf744b of size 35 magma f63e2351 of size 35 magma 1379fc69 of size 35 magma 7621294b of size 35 magma 6f9f99f6 of size 35 magma ec1e3c0c of size 35 magma 2b25aad6 of size 35 magma 9849862a of size 35 magma 63832d10 of size 35 magma 3494b36b of size 35 magma 3849320c of size 35 magma 1a85430f of size 35 magma 0200f931 of size 35 magma 50aedc8b of size 35 magma 56c3abed of size 35 magma 24666984 of size 35 magma fe6492ab of size 35 magma 80ea2cbe of size 35 magma 2523fb68 of size 35 magma 1ad7abc8 of size 35 magma 1a5b6e53 of size 35 magma e954966d of size 35 magma 1961ea85 of size 35 magma afef4e02 of size 35 magma 59644f82 of size 35 magma 92b281c4 of size 35 magma b9f54c86 of size 35 magma 2de6f7cc of size 35 magma da13a3e9 of size 35 magma c747f1fd of size 35 magma 9507f93e of size 35 magma 7c720ff2 of size 35 magma 19b095b6 of size 35 magma 8a256d8b of size 35 magma 611cd748 of size 35 magma d2e9f63b of size 35 magma 2320ff6b of size 35 magma d8a005b5 of size 35 magma 893c0e3d of size 35 magma ca79ef6c of size 35 magma f91c76dc of size 35 magma 8c4d472d of size 35 magma c2667740 of size 35 magma c81b0fc6 of size 35 magma 08c4ff91 of size 35 magma df1aa9fc of size 35 magma 0d20ca8e of size 35 magma 5acd7f59 of size 35 magma 85f7fb35 of size 35 magma 262b8485 of size 35 magma 865f28c7 of size 35 magma 20d6c677 of size 35 magma 636ea8ba of size 35 magma bab24597 of size 35 magma 5af0ce39 of size 35 magma b5e1fbb4 of size 35 magma 2cbb2b69 of size 35 magma d3120e7c of size 35 magma 5a65d769 of size 35 magma 370cd519 of size 35 magma c1ccf681 of size 35 magma 8507a686 of size 35 magma 6d0cdf9c of size 35 magma 18be6a5e of size 35 magma 648d3f9d of size 35 magma c373c820 of size 35 magma 891061cc of size 35 magma b28a0d6f of size 35 magma b1fdba9e of size 35 magma 5680af3e of size 35 magma 6d0c39fc of size 35 magma 4ec9d52b of size 35 magma 37eb0e52 of size 35 magma 910baabb of size 35 magma c5d49944 of size 35 magma d156e48d of size 35 magma 18c39083 of size 35 magma 3c6e3be2 of size 35 magma ceda7d97 of size 35 magma e18fc0fd of size 35 magma 362ea644 of size 35 magma 65f2da2b of size 35 magma 8ede3b8d of size 35 magma ee6a5d64 of size 35 magma 23feb90e of size 35 magma df1300df of size 35 magma 47e5093e of size 35 magma 52857f3c of size 35 magma 13c05b15 of size 35 magma 9647ef98 of size 35 magma dc7da5b4 of size 35 magma 65e2110f of size 35 magma 8e9afc9d of size 35 magma 4993b3ef of size 35 magma 9261d6ea of size 35 magma ddfbc2ea of size 35 magma be23f3f6 of size 35 magma 15b11f3e of size 35 magma d766427c of size 35 magma 91a137fd of size 35 magma e9b60e64 of size 35 magma 9a9aa50f of size 35 magma 0e215124 of size 35 magma e52e8f4b of size 35 magma d6a3a2f9 of size 35 magma eccda6e4 of size 35 magma 1c84ff37 of size 35 magma d0e310b8 of size 35 magma 07e0dc1c of size 35 magma da06beba of size 35 magma 8243ea56 of size 35 magma f89e4e7e of size 35 magma 04faeb93 of size 35 magma 865f32ec of size 35 magma b344b8f5 of size 35 magma b5fa8bb4 of size 35 magma e03b974b of size 35 magma f40e7b8d of size 35 magma b3483c0c of size 35 magma 24c58697 of size 35 magma 54fd7328 of size 35 magma 6eb2cdab of size 35 magma 9c39ea39 of size 35 magma beef095b of size 35 magma 578ebe9b of size 35 magma c9ce982b of size 35 magma 33eb3b1c of size 35 magma 5c7f6af3 of size 35 magma 1530735c of size 35 magma 94e8599f of size 35 magma aa6b86b8 of size 35 magma b6306b17 of size 35 magma e489ba0b of size 35 magma 79a47f20 of size 35 magma 8307868a of size 35 magma a839436f of size 35 magma dc6e7ce0 of size 35 magma 5920b1ee of size 35 magma a86b8442 of size 35 magma 9e8806db of size 35 magma 89efefac of size 35 magma 18df663d of size 35 magma 9930bed3 of size 35 magma 53b80621 of size 35 magma 52b5530a of size 35 magma 04bd807c of size 35 magma a8c9806c of size 35 magma 5a221b8b of size 35 magma ca3ec772 of size 35 magma 34f851e9 of size 35 magma 9ee390db of size 35 magma d0ee58dc of size 35 magma eec65d4e of size 35 magma 433ebb63 of size 35 magma 6f91eb1d of size 35 magma d9ee6132 of size 35 magma 2f49bc8d of size 35 magma 7b9a915c of size 35 magma 94454c80 of size 35 magma ebec5acc of size 35 magma b6b73992 of size 35 magma 90c554f5 of size 35 magma 7f5636d7 of size 35 magma 4788bf30 of size 35 magma 20993c3f of size 35 magma adeb88dd of size 35 magma 9835fe45 of size 35 magma 3e48b29b of size 35 magma f595fa6b of size 35 magma 4a98cca0 of size 35 magma 58c32aab of size 35 magma 5da5af1e of size 35 magma f646f45b of size 35 magma 1d811b4b of size 35 magma 6780e2f3 of size 35 magma 297b4061 of size 35 magma 447d02fe of size 35

Commentary

Size 35 = 5 x 7: the permutation-twisted fibre-bundle family, and how far it is from exhausted. Most known size-35 eq677 magmas (including all 91 of omegaestable's) are "switched 5x7 fibre products": coordinates (i,u), i in F_5, u in F_7, with quotient the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j), and (i,u)*(j,v) = (2i+4j, D(u,v)) if i=j (i,u)*(j,v) = (2i+4j, p^-1(O(p(u),p(v)))) if i!=j where D, O are F_7 affine eq677 laws -- each one of u*v = 4u+v (magma#7981e2df) or 4u+3v (magma#baf8b55c) -- and p is a permutation of the 7-element FIBRE applied on every off-diagonal product. EXACT count of this single-permutation construction. For fixed (D,O), two twists p,p' give isomorphic magmas iff p' = g p r^-1 with g in Aut(O), r in Aut(D). Each of the two F_7 laws has automorphism group {u -> s u : s in F_7*} of order 6, so the classes are the double cosets Aut(O) \ S_7 / Aut(D): exactly 144 of them. The diagonal law D and off law O are isomorphism invariants (the 7-element subalgebras are copies of D; the off-diagonal fibre operation is a copy of O), and the two F_7 laws are non-isomorphic, so the four (D,O) choices give DISJOINT families. Hence this construction yields exactly 4 x 144 = 576 distinct isomorphism classes at size 35. (Checked: the double-coset prediction agrees with direct isomorphism testing on every sampled pair, with no cross-family collisions.) So size 35 is far from exhausted. Of the current 119 size-35 entries, 103 are classes of this construction -- leaving 473 of the 576 single-permutation classes not yet submitted. The other 16 entries (e.g. magma#a9a63e11, magma#4ad1a74f) are NOT of this single-p form, so further families exist beyond the 576: e.g. using a different (forced-compatible) twist on each off-diagonal base-difference, or semilinear fibre maps. Whether every size-35 eq677 magma is a 5x7 fibre bundle is open. [text written by Claude]

last edited by dwrensha at 2026-06-17 12:26:13 · history