Equation 677 Database

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Magma be9113db652f…

magma be9113db652f
Size
399
Isomorphism class hash
be9113db652fda712b7018845cb83f818673e5497f1bdd81fba2177b2639ad75
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 14:17:26
Display reorder
270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,380,327,180,320,301,328,321,302,181,329,182,322,303,330,183,323,304,331,184,315,305,316,332,185,297,324,186,317,298,325,187,318,299,326,188,319,300,189,336,313,294,190,337,314,295,191,338,306,296,192,339,307,288,193,340,308,289,194,341,309,290,195,333,310,291,196,334,311,292,197,335,312,293,391,385,386,392,221,208,132,164,222,133,165,209,223,210,134,166,224,211,126,167,216,212,127,168,128,217,213,169,218,214,129,170,219,215,130,162,220,207,131,163,201,230,141,173,202,231,142,174,203,232,143,175,204,233,135,176,205,225,136,177,206,226,137,178,198,227,138,179,199,228,139,171,200,229,140,172,383,389,390,384,76,237,31,1,77,32,0,238,78,239,33,2,79,240,34,3,80,241,35,4,27,72,242,5,73,234,28,6,74,235,29,7,75,236,30,8,246,85,24,9,247,86,25,10,248,87,26,11,249,88,18,12,250,89,19,13,251,81,20,14,243,82,21,15,244,83,22,16,245,84,23,17,388,398,397,387,348,118,148,342,350,149,344,119,352,120,150,346,354,121,151,349,356,122,152,351,144,358,123,353,343,124,145,355,345,125,146,357,347,117,147,359,111,367,157,361,112,369,158,363,113,371,159,365,114,373,160,366,115,375,161,368,116,377,153,370,108,360,154,372,109,362,155,374,110,364,156,376,394,395,396,393,56,47,263,107,57,264,99,48,58,49,265,100,59,50,266,101,60,51,267,102,268,61,52,103,62,53,269,104,54,45,261,105,55,46,262,106,40,65,256,91,41,66,257,92,42,67,258,93,43,68,259,94,44,69,260,95,36,70,252,96,37,71,253,97,38,63,254,98,39,64,255,90,379,381,378,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#d9195575bdf1df3ba33e2895afc27f36f460f642bc4fe255efa4b21805fb36e7, M = the submagma generated by {0} (19 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-07 14:17:27 · history