Equation 677 Database

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Magma 875f9bd727ad…

magma 875f9bd727ad
Size
707
Isomorphism class hash
875f9bd727addff40afe6a514f87f3d669462b7f4b26792ea126766a16882662
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
2026-10-07 23:45:59
Display reorder
490,489,491,486,487,488,631,144,149,145,146,147,148,92,93,94,95,90,91,44,43,45,46,47,42,200,199,201,202,203,198,186,191,187,188,189,190,97,96,98,99,100,101,171,170,172,173,168,169,215,214,210,211,212,213,273,272,274,275,270,271,70,69,71,66,67,68,304,303,305,301,300,302,426,428,427,429,430,431,521,520,519,517,518,516,468,470,469,473,471,472,435,437,436,432,433,434,390,392,391,395,393,394,462,464,463,467,465,466,399,401,400,398,396,397,336,338,337,341,339,340,347,346,345,344,342,343,608,609,607,606,611,610,637,645,647,697,667,677,696,676,699,698,687,702,706,705,61,60,62,63,64,65,107,102,103,104,105,106,230,229,231,232,233,228,238,237,239,234,235,236,220,219,221,216,217,218,175,174,176,177,178,179,295,299,294,296,297,298,290,288,291,292,293,289,74,73,75,76,77,72,80,79,81,82,83,78,183,182,184,185,180,181,475,474,476,478,479,477,482,481,480,484,485,483,457,456,458,459,460,461,405,407,406,402,403,404,422,421,420,424,425,423,447,449,448,446,444,445,524,523,522,526,527,525,590,588,589,592,593,591,565,566,564,567,568,569,630,633,632,634,649,648,642,635,640,682,681,690,680,660,672,673,674,683,691,700,52,51,53,48,49,50,128,129,130,131,126,127,141,140,142,143,138,139,56,55,57,58,59,54,86,85,87,88,89,84,136,135,137,132,133,134,248,246,249,250,251,247,241,243,245,244,240,242,227,226,222,223,224,225,122,121,123,124,125,120,108,113,109,110,111,112,548,546,547,551,549,550,534,535,536,537,538,539,454,453,455,450,451,452,579,581,580,577,576,578,600,601,602,603,604,605,439,438,440,441,442,443,350,349,348,352,353,351,530,529,528,532,533,531,583,584,582,585,586,587,612,646,617,644,618,638,636,641,643,692,675,688,694,658,668,678,659,693,684,701,34,33,35,30,31,32,5,1,0,2,3,4,278,277,279,280,281,276,316,315,317,312,313,314,114,119,115,116,117,118,307,306,308,309,310,311,268,267,269,265,264,266,8,7,9,10,11,6,26,25,27,28,29,24,258,259,260,261,262,263,36,41,37,38,39,40,540,541,542,544,545,543,561,560,562,558,559,563,570,571,572,573,574,575,492,494,493,495,496,497,414,416,415,419,417,418,514,513,515,510,511,512,499,498,500,501,502,503,386,385,384,388,389,387,594,595,596,598,599,597,628,616,629,615,614,613,639,651,650,704,666,679,703,657,665,685,664,686,689,695,17,16,12,13,14,15,205,206,207,208,209,204,157,156,158,159,160,161,163,162,164,165,166,167,326,328,327,324,325,329,254,253,255,256,257,252,19,18,20,21,22,23,322,321,323,319,318,320,197,196,192,193,194,195,282,283,284,285,286,287,155,154,150,151,152,153,412,411,413,409,410,408,370,369,371,366,367,368,373,372,374,375,376,377,378,380,379,381,382,383,557,556,555,552,554,553,508,507,509,504,505,506,356,355,354,358,359,357,360,362,361,365,363,364,334,333,335,330,332,331,625,619,624,620,622,623,621,627,626,670,656,662,669,653,654,655,652,663,661,671 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = {84, 85, 86, 87, 88, 89, 132} 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 2026-10-07 23:46:00 · history