Equation 677 Database

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Magma f7ae5c857811…

magma f7ae5c857811
Size
707
Isomorphism class hash
f7ae5c8578110d9675f663ae69eace08fd1c287f953f75b35c602189e869daef
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 07:58:22
Display reorder
67,66,68,69,70,71,706,281,277,276,278,279,280,95,94,90,91,92,93,288,289,290,291,292,293,82,81,83,78,79,80,305,304,301,300,302,303,197,196,192,193,194,195,284,282,285,286,287,283,88,87,89,84,85,86,76,75,77,72,73,74,298,297,299,295,294,296,349,348,350,352,353,351,545,544,543,541,542,540,536,535,534,538,539,537,604,603,605,601,600,602,533,532,531,530,528,529,342,344,343,346,347,345,354,356,355,359,357,358,361,360,362,365,363,364,370,369,371,366,367,368,596,594,595,599,597,598,653,650,643,642,651,652,654,655,635,634,703,677,697,704,702,691,701,698,705,699,122,123,124,125,120,121,171,170,172,173,168,169,52,51,53,48,49,50,58,57,59,54,55,56,126,131,127,128,129,130,273,272,274,271,270,275,175,174,176,177,178,179,136,135,137,132,133,134,189,188,190,191,186,187,185,184,180,181,182,183,418,417,419,415,416,414,494,493,492,496,497,495,472,471,473,468,469,470,520,519,521,516,517,518,507,509,508,504,505,506,322,321,323,320,318,319,467,466,465,463,464,462,459,461,460,457,458,456,325,324,326,327,328,329,402,404,403,405,406,407,637,631,639,628,638,621,633,648,646,649,700,696,694,689,673,666,678,668,690,680,98,99,100,101,96,97,235,234,236,237,238,239,103,102,104,105,106,107,203,202,198,199,200,201,204,209,205,206,207,208,246,247,248,249,250,251,19,18,20,21,22,23,12,17,13,14,15,16,267,266,268,269,265,264,30,35,31,32,33,34,567,569,568,565,564,566,570,572,571,573,574,575,432,434,433,437,435,436,580,579,581,577,576,578,445,444,446,448,449,447,588,589,590,593,591,592,554,553,552,556,557,555,451,450,452,455,453,454,393,395,394,392,390,391,583,584,582,585,586,587,625,640,612,636,613,641,626,627,629,630,692,693,686,683,665,670,671,675,681,688,7,8,9,10,11,6,245,244,241,240,242,243,26,25,27,28,29,24,41,40,36,37,38,39,228,233,229,230,231,232,215,214,210,211,212,213,220,219,221,216,217,218,141,140,142,143,138,139,147,146,148,149,144,145,225,224,226,227,222,223,341,340,339,338,336,337,443,442,441,439,440,438,558,560,559,563,561,562,375,377,376,374,372,373,548,547,546,551,549,550,317,316,315,312,313,314,381,383,382,380,378,379,384,386,385,388,389,387,310,309,311,307,306,308,401,400,399,398,396,397,609,610,611,606,608,607,632,644,647,645,695,682,684,687,672,667,674,676,685,679,111,112,113,108,109,110,151,150,152,153,154,155,117,116,118,119,114,115,2,0,3,4,5,1,60,65,61,62,63,64,254,257,253,256,255,252,260,258,261,262,263,259,165,164,166,167,162,163,160,159,161,156,157,158,44,43,45,46,47,42,515,514,513,512,510,511,498,500,499,503,501,502,430,429,431,426,427,428,332,331,330,334,335,333,488,487,486,491,489,490,420,422,421,424,425,423,485,484,483,481,482,480,526,525,527,524,522,523,474,476,475,479,477,478,409,408,410,412,413,411,617,615,614,620,618,619,622,623,616,624,669,659,663,664,656,657,660,658,661,662 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 = {0, 1, 2, 3, 4, 5, 146} 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 07:58:23 · history