Equation 677 Database

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Magma a992276b2f2d…

magma a992276b2f2d
Size
707
Isomorphism class hash
a992276b2f2d02a309b651035a70aed83317dbf5d1903e2d940fc3838821b45f
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 21:09:14
Display reorder
559,558,560,561,562,563,637,111,110,112,113,108,109,219,218,221,216,217,220,196,195,197,192,193,194,5,4,1,0,2,3,166,165,167,162,163,164,82,81,83,78,79,80,173,172,168,169,170,171,20,19,21,22,23,18,266,265,267,268,269,264,11,10,6,7,8,9,302,300,303,304,305,301,498,497,499,495,496,494,588,590,589,586,587,591,481,480,479,478,476,477,387,386,388,384,385,383,382,381,380,378,379,377,529,531,530,534,532,533,535,537,536,540,538,539,544,592,545,548,546,547,594,593,595,598,596,597,632,643,633,616,609,610,607,644,647,697,667,680,698,678,699,700,690,703,705,706,191,190,186,187,188,189,75,74,77,72,73,76,174,179,175,176,177,178,204,209,205,206,207,208,180,185,181,182,183,184,24,29,25,26,27,28,271,270,272,273,274,275,286,285,287,282,283,284,95,94,90,91,92,93,84,89,85,86,87,88,46,45,47,42,43,44,473,475,474,470,471,472,506,508,507,509,510,511,399,398,397,396,394,395,566,567,565,568,569,570,401,400,402,403,404,405,446,445,444,442,443,441,520,519,518,522,523,521,469,468,467,465,466,464,407,406,408,411,409,410,631,628,629,630,649,650,626,642,627,682,681,695,683,658,674,673,668,684,694,701,54,59,55,56,57,58,147,146,149,144,145,148,127,126,128,129,130,131,288,293,289,290,291,292,136,135,137,132,133,134,199,198,200,201,202,203,50,49,51,52,53,48,107,106,102,103,104,105,227,226,222,223,224,225,254,253,255,256,257,252,261,260,262,263,258,259,564,367,366,370,368,369,359,358,357,356,354,355,362,361,360,365,363,364,434,433,432,431,429,430,347,346,345,343,344,342,605,604,603,601,602,600,425,424,423,427,428,426,550,549,551,552,553,554,555,412,413,416,414,415,608,646,625,645,623,615,624,613,614,693,677,687,689,659,670,676,661,692,679,696,236,235,237,238,239,234,276,281,278,279,280,277,16,15,17,12,13,14,309,308,310,311,306,307,247,246,248,249,250,251,313,312,314,315,316,317,298,297,299,294,295,296,96,101,97,98,99,100,39,38,40,41,36,37,32,31,33,34,35,30,141,140,142,143,138,139,436,435,437,439,440,438,450,452,451,447,448,449,372,371,373,375,376,374,454,556,453,457,455,456,459,458,460,461,462,463,524,526,525,557,527,528,421,420,422,417,418,419,513,512,514,515,516,517,337,336,338,341,339,340,606,618,621,622,619,620,617,651,648,702,672,685,704,664,665,675,657,688,686,691,66,71,67,68,69,70,229,228,231,232,233,230,210,215,211,212,213,214,120,125,121,122,123,124,326,328,327,324,325,329,242,241,243,244,245,240,62,61,63,64,65,60,323,322,319,318,320,321,158,157,159,160,161,156,153,152,154,155,150,151,117,116,118,119,114,115,331,332,330,333,334,335,389,391,390,392,393,599,572,571,573,575,576,574,348,350,349,351,352,353,581,580,582,583,584,585,577,579,578,543,541,542,487,486,485,483,484,482,490,489,488,492,493,491,500,502,501,504,505,503,641,638,640,639,611,636,612,634,635,669,656,660,671,654,652,655,653,662,663,666 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, M = {114, 115, 116, 117, 118, 119, 135} 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 21:09:15 · history