Equation 677 Database

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Magma 4675624f5791…

magma 4675624f5791
Size
705
Isomorphism class hash
4675624f579130eace91f2c47c08cb4f49769e6243af6d37272835694727e200
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 15:14:06
Display reorder
660,483,165,387,459,447,484,163,388,460,448,482,164,386,458,446,486,161,390,462,450,162,487,391,463,451,160,485,389,461,449,481,171,385,457,445,479,169,383,455,443,480,170,384,456,444,167,477,381,453,441,168,478,382,454,442,166,476,380,452,440,666,665,668,663,143,50,435,79,17,144,48,436,80,15,142,49,434,78,16,146,53,438,82,13,51,147,439,83,14,52,145,437,81,12,141,56,433,77,23,139,54,431,75,21,140,55,432,76,22,59,137,429,73,19,57,138,430,74,20,58,136,428,72,18,690,687,685,686,471,309,243,507,351,472,310,241,508,352,470,308,242,506,350,474,312,239,510,354,313,475,240,511,355,311,473,238,509,353,469,315,234,505,349,467,316,232,503,347,468,314,233,504,348,318,465,237,501,345,319,466,235,502,346,317,464,236,500,344,669,661,667,670,527,89,399,71,423,528,87,400,69,424,526,88,398,70,422,530,85,402,67,426,86,531,403,68,427,84,529,401,66,425,525,95,397,62,421,523,93,395,60,419,524,94,396,61,420,91,521,393,65,417,92,522,394,63,418,90,520,392,64,416,673,676,679,674,207,106,575,181,195,205,107,576,182,193,206,105,574,183,194,203,102,578,180,191,103,204,579,178,192,104,202,577,179,190,198,97,573,172,186,196,98,571,173,184,197,96,572,174,185,100,201,569,175,189,101,199,570,176,187,99,200,568,177,188,672,662,664,671,337,301,375,563,551,335,299,376,564,552,336,300,374,562,550,333,297,378,566,554,298,334,379,567,555,296,332,377,565,553,343,307,373,561,549,341,305,371,559,547,342,306,372,560,548,303,339,369,557,545,304,340,370,558,546,302,338,368,556,544,697,696,693,694,280,268,635,519,288,646,269,647,644,645,281,270,634,518,289,653,271,655,652,654,272,657,659,656,658,273,648,651,649,650,286,274,633,513,293,287,275,631,514,294,285,276,632,512,295,277,282,629,516,292,278,283,630,517,290,279,284,628,515,291,702,701,703,704,129,209,108,121,599,636,210,109,637,600,128,208,110,120,598,640,212,111,641,602,213,642,112,643,603,211,639,113,638,601,135,215,114,124,597,133,216,115,122,595,134,214,116,123,596,218,131,117,127,593,219,132,118,125,594,217,130,119,126,592,700,698,699,695,587,158,411,539,366,588,159,412,540,367,586,157,410,538,365,590,154,414,542,362,155,591,415,543,363,156,589,413,541,364,585,149,409,537,357,583,150,407,535,358,584,148,408,536,356,152,581,405,533,360,153,582,406,534,361,151,580,404,532,359,680,684,682,675,36,227,611,495,27,37,228,612,496,28,38,226,610,494,29,39,230,614,498,26,231,40,615,499,24,229,41,613,497,25,42,225,609,493,33,43,223,607,491,34,44,224,608,492,35,221,45,605,489,32,222,46,606,490,30,220,47,604,488,31,678,681,677,683,329,9,252,260,623,330,10,250,261,624,331,11,251,259,622,328,8,255,256,626,6,326,253,257,627,7,327,254,258,625,320,1,247,266,621,321,0,248,267,619,322,2,249,265,620,3,323,246,262,617,4,324,244,263,618,5,325,245,264,616,688,692,689,691 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#0c204955552ad126415d2d3170da1bc3e83549814dfd47378340ca39d32aede4, 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 15:14:07 · history