Equation 677 Database

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Magma 3786da48d790…

magma 3786da48d790
Size
707
Isomorphism class hash
3786da48d7901842a517e71df6f54d540cc7f988cf819ba00da7d92c16f4d60a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 18:55:37
Display reorder
447,446,445,451,448,449,639,331,332,333,334,335,330,99,98,100,101,96,97,84,89,85,86,87,88,157,156,158,159,160,161,206,205,207,208,209,204,219,218,220,221,216,217,194,193,195,196,197,192,48,53,49,50,51,52,47,46,42,43,44,45,272,271,273,274,275,270,359,354,355,356,358,357,214,213,215,210,211,212,369,368,370,532,367,366,457,459,458,456,454,455,361,362,360,364,365,363,476,475,477,473,474,472,493,495,494,490,491,492,481,483,482,478,479,480,551,553,552,555,568,554,556,558,557,560,561,559,617,615,607,609,616,611,633,625,683,661,648,658,680,681,700,698,699,706,701,703,250,251,246,247,248,249,108,113,109,110,111,112,39,38,40,41,36,37,75,74,76,77,72,73,137,136,132,133,134,135,122,121,123,124,125,120,151,150,152,153,154,155,141,140,142,143,138,139,303,302,304,305,300,301,6,11,7,8,9,10,327,326,328,329,324,325,318,323,319,320,321,322,496,498,497,499,500,501,569,408,407,405,406,404,417,416,415,418,419,420,412,414,413,409,410,411,423,422,421,426,424,425,427,429,428,430,431,432,520,522,521,524,525,523,435,434,433,436,437,438,614,610,613,618,608,606,630,612,684,650,655,653,688,667,685,666,682,702,689,687,65,60,61,62,63,64,236,235,237,238,239,234,230,229,231,232,233,228,55,54,56,57,58,59,268,267,269,264,265,266,287,286,282,283,284,285,24,29,25,26,27,28,128,127,129,130,131,126,103,102,104,105,106,107,78,83,79,80,81,82,71,70,66,67,68,69,30,35,31,32,33,34,583,584,582,585,586,587,589,590,588,593,591,592,395,397,396,393,394,392,510,509,508,513,511,512,401,403,402,398,399,400,541,540,539,544,542,543,563,562,564,567,565,566,519,518,517,514,515,516,622,629,624,623,627,628,632,626,671,665,664,656,676,669,694,697,691,704,670,690,316,317,312,313,314,315,309,308,310,311,306,307,294,299,295,296,297,298,262,261,263,258,259,260,148,147,149,144,145,146,336,337,338,339,340,341,119,118,114,115,116,117,293,292,288,289,290,291,2,0,3,4,5,1,254,253,255,256,257,252,353,352,349,348,350,351,342,343,344,345,346,347,444,443,442,441,439,440,570,571,572,573,574,575,528,527,526,529,530,531,600,601,602,604,605,603,594,595,596,598,599,597,506,505,507,503,504,502,578,576,577,579,580,581,548,550,549,546,547,545,621,635,620,619,631,634,643,644,678,674,649,677,675,673,696,692,679,705,693,695,177,178,179,174,175,176,183,182,184,185,180,181,241,240,242,243,244,245,200,199,201,202,203,198,191,190,186,187,188,189,281,280,276,277,278,279,13,12,14,15,16,17,227,226,222,223,224,225,94,93,95,90,91,92,165,164,166,167,162,163,173,172,168,169,170,171,23,22,18,19,20,21,391,390,389,388,386,387,484,486,485,489,487,488,465,464,463,460,461,462,470,469,471,467,468,466,538,537,536,535,533,534,453,450,452,378,379,377,376,375,374,371,372,373,381,380,382,385,383,384,640,641,638,636,637,642,645,646,668,652,647,651,672,662,663,657,659,686,654,660 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = {108, 109, 110, 111, 112, 113, 131} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-08 18:55:38 · history