Equation 677 Database

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Magma 923115147791…

magma 923115147791
Size
705
Isomorphism class hash
923115147791366deecbf643f185daf5202c83dd534f72eb0cae9f52d1bdf12e
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 18:14:21
Display reorder
660,518,30,156,350,260,516,31,348,157,258,517,32,158,349,259,33,521,159,353,263,34,519,160,351,261,35,520,161,352,262,524,36,154,356,266,522,37,155,354,264,523,38,153,355,265,39,527,150,359,269,40,525,151,357,267,41,526,152,358,268,666,664,661,669,201,470,335,221,227,202,468,219,333,225,203,469,334,220,226,473,200,331,217,223,471,198,332,218,224,472,199,330,216,222,207,476,326,212,233,208,474,324,210,231,209,475,325,211,232,479,206,329,215,229,477,204,327,213,230,478,205,328,214,228,687,690,692,688,554,163,59,446,494,552,164,444,57,492,553,162,58,445,493,166,557,55,449,497,167,555,56,447,495,165,556,54,448,496,560,169,65,452,500,558,170,63,450,498,559,168,64,451,499,172,563,61,455,503,173,561,62,453,501,171,562,60,454,502,671,667,668,670,340,434,15,400,410,341,432,401,16,408,339,433,17,399,409,437,336,14,396,413,435,337,12,397,411,436,338,13,398,412,346,440,6,406,416,347,438,7,407,414,345,439,8,405,415,443,342,9,402,419,441,343,10,403,417,442,344,11,404,418,678,674,677,673,290,276,97,365,374,288,277,363,98,372,289,278,96,364,373,279,293,100,361,377,280,291,101,362,375,281,292,99,360,376,296,282,95,371,380,294,283,93,369,378,295,284,94,370,379,285,299,91,367,383,286,297,92,368,381,287,298,90,366,382,672,662,665,663,482,458,47,28,542,480,456,29,45,540,481,457,46,27,541,461,485,43,24,545,459,483,44,25,543,460,484,42,26,544,488,464,53,19,548,486,462,51,20,546,487,463,52,18,547,467,491,49,22,551,465,489,50,23,549,466,490,48,21,550,694,693,697,695,568,3,134,271,584,569,4,272,132,582,567,5,133,270,583,2,564,137,274,587,1,565,135,275,585,0,566,136,273,586,644,645,129,646,647,639,636,130,637,638,640,641,131,642,643,657,656,128,658,659,648,649,126,650,651,652,653,127,654,655,701,703,704,702,572,117,113,303,590,570,118,304,111,588,571,119,112,305,589,116,575,109,302,593,114,573,110,300,591,115,574,108,301,592,578,123,104,309,596,576,124,102,310,594,577,125,103,311,595,122,581,107,308,599,120,579,105,306,597,121,580,106,307,598,696,700,699,698,186,386,147,530,246,187,384,528,148,247,188,385,149,529,248,389,189,146,533,249,387,190,144,531,250,388,191,145,532,251,192,392,138,536,252,193,390,139,534,253,194,391,140,535,254,395,195,141,539,255,393,196,142,537,256,394,197,143,538,257,676,680,682,684,320,506,79,626,602,318,504,624,80,600,319,505,78,625,601,509,323,82,629,605,507,321,83,627,603,508,322,81,628,604,315,512,85,632,608,316,510,86,630,606,317,511,84,631,607,515,314,88,635,611,513,312,89,633,609,514,313,87,634,610,679,683,681,675,70,614,239,422,184,71,612,420,237,185,69,613,238,421,183,617,66,235,425,180,615,67,236,423,181,616,68,234,424,182,76,620,245,428,175,77,618,243,426,176,75,619,244,427,174,623,72,241,431,178,621,73,242,429,179,622,74,240,430,177,691,686,689,685 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#6da5e6765bc0adc27e9eb05052cc3d9b74fd6a5fdc541eafc0e7aaffee5eac36, 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 18:14:22 · history