Equation 677 Database

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Magma 662ac68c0176…

magma 662ac68c0176
Size
707
Isomorphism class hash
662ac68c0176b95487bd165506c3815f489d2804e372eeab73054210125d073b
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 18:07:41
Display reorder
83,82,78,79,80,81,706,288,290,291,292,293,289,35,34,30,31,32,33,304,303,305,301,300,302,285,284,286,287,282,283,118,117,119,114,115,116,58,57,59,54,55,56,223,227,222,224,225,226,165,164,166,167,162,163,97,96,98,99,100,101,298,299,294,296,297,295,333,335,334,332,330,331,572,570,571,573,574,575,380,379,378,382,383,381,358,357,359,356,354,355,580,579,581,578,577,576,427,426,428,431,429,430,419,418,417,415,416,414,523,522,524,525,526,527,468,470,469,473,471,472,310,309,311,307,306,308,612,610,608,611,606,607,635,630,637,633,682,683,697,698,705,696,699,702,704,703,240,243,244,245,241,242,71,70,66,67,68,69,248,246,249,250,251,247,127,126,128,129,130,131,256,255,257,253,252,254,46,45,47,42,43,44,204,209,205,206,207,208,236,234,237,238,239,235,53,52,48,49,50,51,154,153,155,150,151,152,542,540,541,544,545,543,406,405,407,404,402,403,399,401,400,398,396,397,528,529,530,533,531,532,488,487,486,489,490,491,482,481,480,483,484,485,437,436,435,433,434,432,536,534,535,538,539,537,342,344,343,347,345,346,509,508,507,505,506,504,614,615,618,613,619,617,620,616,631,632,687,700,701,669,686,670,671,675,673,685,280,277,276,278,279,281,187,186,188,189,190,191,213,212,214,215,210,211,185,184,180,181,182,183,91,90,92,93,94,95,216,221,217,218,219,220,125,124,120,121,122,123,39,38,40,41,36,37,27,26,28,29,24,25,60,65,61,62,63,64,326,325,324,328,329,327,323,322,321,318,319,320,563,562,561,558,560,559,413,412,411,408,409,410,312,314,313,316,317,315,585,587,586,582,584,583,463,462,464,465,466,467,565,566,564,569,567,568,552,553,554,555,556,557,349,348,350,351,352,353,625,624,629,626,627,622,634,623,636,628,672,695,692,674,679,681,666,684,667,693,203,199,200,201,202,198,195,194,196,197,192,193,135,134,136,137,132,133,3,2,4,5,1,0,263,262,259,258,260,261,147,146,148,149,144,145,138,143,139,140,141,142,269,268,265,264,266,267,275,274,271,270,272,273,73,72,74,75,76,77,458,457,456,460,461,459,492,494,493,496,497,495,517,516,518,519,520,521,501,503,502,499,500,498,336,338,337,340,341,339,590,588,589,591,592,593,549,551,550,548,547,546,512,511,510,514,515,513,598,597,599,595,594,596,603,605,604,602,601,600,638,649,621,639,651,640,647,653,646,654,676,688,694,680,691,678,668,690,677,689,233,229,230,231,232,228,6,11,7,8,9,10,169,168,170,171,172,173,107,106,102,103,104,105,112,111,113,108,109,110,157,156,158,159,160,161,176,175,177,178,179,174,18,23,19,20,21,22,14,13,15,16,17,12,89,88,84,85,86,87,395,394,393,391,392,390,449,448,447,444,445,446,366,368,367,371,369,370,451,450,452,455,453,454,365,364,363,360,361,362,422,421,420,423,424,425,388,387,389,384,385,386,375,377,376,374,372,373,440,439,438,442,443,441,475,474,476,477,478,479,641,643,650,609,652,645,648,644,642,655,656,659,664,660,661,663,658,662,657,665 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#b487dc9287fe904f43c970fc4391e1719f627a657dc9e65b0768351b07a69a58, M = {60, 61, 62, 63, 64, 65, 144} 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 18:07:42 · history