Equation 677 Database

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Magma aa88111ce87e…

magma aa88111ce87e
Size
707
Isomorphism class hash
aa88111ce87e97506919fc9a3c487d66e2605a274aca807bb97a1f7057d5971f
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 21:05:17
Display reorder
506,505,504,508,509,507,634,125,124,120,121,122,123,83,78,79,80,81,82,44,43,45,46,47,42,193,192,194,195,196,191,231,230,232,233,228,229,240,241,242,243,244,245,71,70,66,67,68,69,236,234,237,238,239,235,207,206,202,203,204,205,24,29,25,26,27,28,313,317,312,314,315,316,528,530,529,525,526,527,409,408,410,411,412,413,418,417,419,414,415,416,432,434,433,435,436,437,473,472,471,468,469,470,422,421,420,424,425,423,407,406,405,402,403,404,399,401,400,398,396,397,430,429,431,427,428,426,608,609,611,612,607,610,638,645,647,699,670,678,697,675,696,698,687,704,705,706,19,18,20,21,22,23,255,256,257,252,253,254,246,251,247,248,249,250,37,36,38,39,40,41,297,296,298,299,295,294,77,76,72,73,74,75,133,132,134,135,136,137,53,52,48,49,50,51,142,141,143,138,139,140,63,62,64,65,60,61,57,56,58,59,54,55,367,366,368,370,371,369,571,572,570,575,573,574,445,444,446,447,448,449,382,381,383,379,380,378,519,521,520,517,518,516,394,393,395,390,391,392,386,385,384,387,388,389,588,589,590,591,592,593,577,578,576,579,580,581,637,639,635,632,648,649,642,636,640,683,680,688,681,658,669,666,671,682,691,700,148,147,149,144,145,146,113,108,109,110,111,112,269,268,265,264,266,267,114,119,115,116,117,118,130,129,131,126,127,128,167,166,162,163,164,165,157,156,158,159,160,161,181,180,182,183,184,179,155,154,150,151,152,153,102,107,103,104,105,106,187,186,188,189,190,185,479,478,477,476,474,475,480,482,481,485,483,484,560,558,559,562,563,561,489,491,490,486,487,488,600,601,602,605,603,604,464,463,462,466,467,465,536,534,535,537,538,539,496,495,497,492,493,494,582,583,584,586,587,585,613,646,614,644,616,615,631,641,643,692,677,690,694,657,668,679,660,693,684,701,280,279,281,276,277,278,275,270,271,272,273,274,211,210,212,213,208,209,309,308,310,311,306,307,96,101,97,98,99,100,303,302,304,305,301,300,85,84,86,87,88,89,91,90,92,93,94,95,35,34,30,31,32,33,12,17,13,14,15,16,261,260,262,263,259,258,335,334,333,332,331,330,543,542,544,540,541,545,567,569,568,566,565,564,553,554,552,555,556,557,461,460,459,456,457,458,514,513,515,510,511,512,546,547,548,551,549,550,533,532,531,524,522,523,595,596,594,597,598,599,627,606,626,629,633,628,630,651,650,702,667,676,703,661,665,685,664,689,686,695,10,9,11,6,7,8,218,221,214,215,216,217,175,178,176,177,174,220,225,224,226,227,222,223,326,328,327,324,325,329,288,289,290,291,292,293,2,0,3,4,5,1,318,319,320,321,322,323,168,173,169,170,171,172,219,201,197,198,199,200,283,287,282,284,285,286,453,455,454,450,451,452,438,440,439,443,441,442,337,336,338,339,340,341,364,363,365,361,362,360,342,344,343,346,347,345,358,357,359,354,355,356,350,349,348,351,352,353,373,372,374,375,376,377,502,501,503,499,500,498,618,620,619,622,623,621,617,624,625,674,656,663,672,653,652,655,654,662,659,673 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#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = {78, 79, 80, 81, 82, 83, 133} 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 21:05:18 · history