Equation 677 Database

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Magma 7775715c80c7…

magma 7775715c80c7
Size
705
Isomorphism class hash
7775715c80c72a1dcbfb4839072894e1215c41dc1808d2443b964eed6d2818f0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:04:33
Display reorder
660,480,178,539,420,100,481,179,540,421,101,482,180,541,422,99,479,181,538,419,103,477,182,536,417,104,183,478,537,418,102,530,471,176,411,98,531,472,177,412,96,532,473,175,413,97,474,533,172,414,94,475,534,173,415,95,476,535,174,416,93,663,671,666,665,456,214,408,287,35,457,215,409,285,33,458,216,410,286,34,455,217,407,290,31,453,218,405,288,32,219,454,406,289,30,399,447,212,282,26,400,448,213,283,24,401,449,211,284,25,450,402,208,281,29,451,403,209,279,27,452,404,210,280,28,690,685,686,687,326,110,635,303,396,324,108,636,304,397,325,109,637,305,398,322,106,634,306,395,323,107,632,307,393,105,321,633,308,394,626,317,116,309,387,627,315,114,310,388,628,316,115,311,389,320,629,112,312,390,318,630,113,313,391,319,631,111,314,392,662,661,672,668,225,42,88,297,3,223,43,89,298,8,224,44,87,299,9,221,45,91,300,1,222,46,92,301,0,47,220,90,302,2,86,231,40,295,6,84,229,41,296,10,85,230,39,294,5,227,82,36,291,4,228,83,37,292,7,226,81,38,293,11,673,682,676,680,587,233,611,563,468,588,234,612,564,469,589,232,613,565,470,586,236,610,562,467,584,237,608,560,465,235,585,609,561,466,602,578,239,554,459,603,579,240,555,460,604,580,238,556,461,581,605,242,557,462,582,606,243,558,463,583,607,241,559,464,667,664,670,669,432,14,551,170,515,433,12,552,171,516,434,13,553,169,517,431,17,550,166,514,429,15,548,167,512,16,430,549,168,513,542,423,20,161,506,543,424,18,162,507,544,425,19,160,508,426,545,23,164,509,427,546,21,165,510,428,547,22,163,511,693,695,697,694,647,132,501,150,505,655,133,654,653,652,659,134,656,658,657,646,131,502,151,141,644,129,503,152,142,130,645,504,153,143,499,638,138,154,148,500,639,139,155,149,498,640,140,156,147,641,495,137,157,144,642,496,135,158,145,643,497,136,159,146,703,701,702,704,265,186,250,254,527,266,184,648,649,528,264,185,650,651,529,261,189,251,72,526,262,187,252,73,524,188,263,253,74,525,248,256,192,75,518,249,257,190,76,519,247,255,191,77,520,259,244,195,78,521,260,245,193,79,522,258,246,194,80,523,700,696,699,698,384,67,350,374,362,385,68,348,372,360,386,66,349,373,361,383,70,346,370,358,381,71,347,371,359,69,382,345,369,357,341,375,65,365,353,339,376,63,363,351,340,377,64,364,352,378,344,61,368,356,379,342,62,366,354,380,343,60,367,355,678,681,683,674,492,269,444,623,199,493,267,445,624,200,494,268,446,625,201,491,272,443,622,198,489,270,441,620,196,271,490,442,621,197,435,483,275,614,205,436,484,273,615,206,437,485,274,616,207,486,438,278,617,204,487,439,276,618,202,488,440,277,619,203,684,679,675,677,122,335,52,599,575,120,333,53,600,576,121,334,51,601,577,118,338,48,598,574,119,336,49,596,572,337,117,50,597,573,58,128,330,590,566,59,126,331,591,567,57,127,332,592,568,124,54,329,593,569,125,55,327,594,570,123,56,328,595,571,688,692,689,691 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#01253a2afae29ad04ad4e5938d81c583acd3aeb3895dbf3461a9c0b97e71e908, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 15:04:34 · history