Equation 677 Database

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Magma 0ac32c0d522a…

magma 0ac32c0d522a
Size
707
Isomorphism class hash
0ac32c0d522a95f1a24dbbd14dbe7b528853234816bb5c87e798b97d566e50ed
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
2026-10-06 14:51:48
Display reorder
162,164,163,167,165,166,639,181,180,185,183,184,182,55,54,56,59,57,58,240,242,241,244,245,243,248,246,247,249,250,251,255,257,256,252,254,253,51,53,52,49,50,48,134,133,132,135,136,137,131,130,129,128,126,127,143,142,141,140,138,139,145,144,146,148,149,147,484,483,485,480,481,482,587,585,589,591,593,582,583,592,584,586,588,590,343,342,344,345,346,347,479,478,474,475,476,477,390,395,391,392,393,394,577,576,578,579,580,581,506,505,507,508,509,504,560,559,561,562,563,558,518,517,519,520,521,516,617,614,613,606,611,608,641,618,633,642,699,676,704,696,687,688,673,698,703,697,24,26,28,29,27,25,231,233,232,229,230,228,60,61,62,65,63,64,259,258,260,262,263,261,277,276,278,281,279,280,16,15,17,14,12,13,87,89,88,85,86,84,94,93,95,91,92,90,66,68,67,71,69,70,34,33,35,31,32,30,355,354,356,357,358,359,333,332,334,335,330,331,529,528,530,531,532,533,572,571,573,574,575,570,404,403,405,406,407,402,468,473,469,470,471,472,515,514,510,511,512,513,503,502,498,499,500,501,431,430,426,427,428,429,449,448,444,445,446,447,647,654,646,626,653,635,643,619,636,634,663,677,671,669,674,660,661,658,681,657,21,23,19,20,18,22,287,283,282,284,285,286,40,39,41,38,36,37,234,236,235,237,238,239,205,204,206,209,207,208,100,99,101,98,96,97,80,79,78,81,82,83,77,76,75,74,72,73,189,191,190,186,187,188,176,175,174,179,177,178,432,437,433,434,435,436,313,312,314,315,316,317,553,552,554,555,556,557,601,599,603,605,594,596,307,311,306,308,309,310,602,600,604,595,597,598,322,321,323,318,319,320,385,384,386,387,388,389,409,408,410,411,412,413,362,361,363,364,365,360,645,650,655,625,656,638,629,620,644,631,683,678,684,685,679,665,689,686,690,666,118,117,116,115,114,119,220,219,221,218,216,217,193,192,194,197,195,196,155,154,153,152,150,151,292,291,293,290,288,289,223,222,224,227,225,226,43,42,44,47,45,46,122,120,121,125,123,124,2,0,1,5,3,4,10,9,11,7,8,6,337,336,338,339,340,341,524,523,525,526,527,522,566,565,567,568,569,564,442,441,443,438,439,440,348,353,349,350,351,352,496,495,497,492,493,494,452,451,453,454,455,450,491,490,486,487,488,489,457,456,458,459,460,461,399,398,400,401,396,397,651,648,649,628,652,637,632,615,640,627,667,668,672,670,680,675,662,664,659,682,210,212,214,215,213,211,112,111,113,110,108,109,202,201,203,200,198,199,265,264,266,268,269,267,158,157,156,159,160,161,274,273,275,272,270,271,302,300,301,303,304,305,171,173,172,168,169,170,102,104,103,105,106,107,296,294,295,299,297,298,422,421,423,424,425,420,369,368,370,371,366,367,539,538,534,535,536,537,328,327,329,324,325,326,417,416,418,419,414,415,540,545,541,542,543,544,466,465,467,462,463,464,374,373,375,376,377,372,378,383,379,380,381,382,546,551,547,548,549,550,616,623,612,607,624,610,621,609,630,622,702,692,706,695,693,700,691,701,705,694 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#ca4e87f44b5aa8ee937e3111d7e18929d38c701d18b6266af0f19751e7c29bcd, M = {54, 55, 56, 57, 58, 59, 128} 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 2026-10-06 14:51:49 · history