Equation 677 Database

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Magma 4781d963d29e…

magma 4781d963d29e
Size
705
Isomorphism class hash
4781d963d29eb61ab1922e36b7584b154f88213ca38c684e668898a58b3f1e7e
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 18:09:23
Display reorder
660,44,216,85,609,444,83,217,607,442,45,215,46,84,608,443,43,88,219,605,440,86,41,220,606,441,87,42,218,604,439,214,50,600,80,435,212,51,598,81,433,213,52,599,82,434,49,210,603,79,438,47,211,601,77,436,78,48,209,602,437,670,668,664,671,561,109,259,252,585,257,107,253,583,559,108,560,258,251,584,557,262,112,255,581,260,558,110,256,582,261,556,111,254,580,104,552,250,265,576,105,550,248,263,574,106,551,249,264,575,555,103,246,268,579,553,101,247,266,577,267,554,102,245,578,687,685,688,689,549,14,379,456,480,377,15,454,478,547,16,548,378,455,479,545,375,13,452,476,376,546,11,453,477,374,544,12,451,475,5,540,447,370,471,6,538,445,368,469,7,539,446,369,470,543,8,450,373,474,541,9,448,371,472,372,542,10,449,473,669,663,666,665,408,149,501,597,573,499,150,595,571,406,151,407,500,596,572,404,497,152,593,569,498,405,153,594,570,496,403,154,592,568,155,399,588,492,564,156,397,586,490,562,157,398,587,491,563,402,158,591,495,567,400,159,589,493,565,494,401,160,590,566,674,677,680,681,338,164,621,355,525,619,165,353,523,339,166,340,620,354,524,341,617,163,351,521,618,342,161,352,522,616,343,162,350,520,170,336,346,612,516,171,337,344,610,514,172,335,345,611,515,332,169,349,615,519,333,167,347,613,517,614,334,168,348,518,662,672,667,661,432,320,191,357,207,192,321,358,208,430,322,431,193,356,206,428,194,323,360,203,195,429,324,361,204,196,427,325,359,205,326,423,363,189,198,327,421,364,190,199,328,422,362,188,197,426,329,366,185,201,424,330,367,186,202,187,425,331,365,200,696,695,698,693,658,122,657,656,659,651,123,650,649,648,124,654,653,652,655,487,306,121,296,271,307,488,119,297,269,305,489,120,298,270,113,482,291,301,274,114,483,292,299,272,115,481,290,300,273,485,116,294,304,277,486,117,295,302,275,303,484,118,293,276,702,703,701,704,646,128,513,396,647,511,129,394,642,643,130,645,512,395,644,638,509,127,392,639,510,640,125,393,641,508,637,126,391,636,134,383,387,504,3,135,384,385,502,0,136,382,386,503,2,634,133,390,507,635,380,131,388,505,4,506,381,132,389,1,700,697,699,694,142,23,468,420,633,466,24,418,631,140,25,141,467,419,632,138,464,26,416,629,465,139,27,417,630,463,137,28,415,628,21,148,411,459,624,22,146,409,457,622,20,147,410,458,623,144,17,414,462,627,145,18,412,460,625,461,143,19,413,626,673,676,684,675,244,287,537,38,227,535,288,39,228,242,289,243,536,40,229,240,533,286,37,230,534,241,284,35,231,532,239,285,36,232,278,235,29,528,225,279,233,30,526,226,280,234,31,527,224,238,281,32,531,221,236,282,33,529,222,530,237,283,34,223,679,678,682,683,93,174,69,53,314,70,175,54,315,94,173,92,68,55,316,89,65,177,56,317,66,90,178,57,318,67,91,176,58,319,180,99,59,75,312,181,100,60,76,313,179,98,61,74,311,95,183,62,71,308,96,184,63,72,309,73,97,182,64,310,690,691,686,692 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#65ec2d14586b016399098bfd783683584e63e97f4655962a7b7e32e1fef46a76, 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 18:09:24 · history