Equation 677 Database

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Magma 83df0e2d17b3…

magma 83df0e2d17b3
Size
705
Isomorphism class hash
83df0e2d17b34417b38facbf7aac19cae03ee648fbaab3b025664745651a3f7d
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 21:17:52
Display reorder
660,171,358,418,382,324,172,359,419,383,322,173,360,384,420,323,174,361,421,385,327,175,362,422,386,325,176,363,423,387,326,177,356,416,380,319,178,357,417,381,320,179,355,415,379,321,180,352,412,376,318,181,353,413,377,316,182,354,414,378,317,663,665,662,664,95,454,406,39,231,93,455,407,40,229,94,456,41,408,230,98,457,409,42,227,96,458,410,43,228,97,459,411,44,226,90,452,404,37,222,91,453,405,38,220,92,451,403,36,221,89,448,400,33,225,87,449,401,34,223,88,450,402,35,224,689,688,685,687,6,557,346,196,526,7,558,347,197,527,5,559,195,348,528,2,560,349,199,529,3,561,350,200,530,4,562,351,198,531,12,555,344,202,524,13,556,345,203,525,11,554,343,201,523,8,551,340,205,520,9,552,341,206,521,10,553,342,204,522,669,661,668,670,104,254,394,261,241,102,255,395,259,242,103,253,260,396,243,100,250,397,257,240,101,251,398,258,238,99,252,399,256,239,110,245,392,267,232,108,246,393,265,233,109,244,391,266,234,106,248,388,263,235,107,249,389,264,236,105,247,390,262,237,676,675,678,673,111,478,588,600,490,112,479,589,601,491,113,480,602,590,492,114,481,591,603,493,115,482,592,604,494,116,483,593,605,495,117,476,586,598,488,118,477,587,599,489,119,475,585,597,487,120,472,582,594,484,121,473,583,595,485,122,474,584,596,486,666,671,667,672,162,576,337,514,189,163,577,338,515,190,164,578,516,339,191,161,579,336,517,192,159,580,334,518,193,160,581,335,519,194,168,574,328,512,187,169,575,329,513,188,170,573,330,511,186,167,570,331,508,183,165,571,332,509,184,166,572,333,510,185,698,696,693,695,52,538,0,569,14,53,643,642,640,641,51,645,646,644,647,55,648,649,650,651,56,652,653,654,655,54,656,657,658,659,50,533,58,564,20,48,534,59,565,18,49,532,57,563,19,46,536,61,567,16,47,537,62,568,17,45,535,60,566,15,702,701,704,703,71,628,629,430,129,69,630,631,431,130,70,633,432,632,131,74,634,635,433,132,72,636,637,434,133,73,638,639,435,134,66,625,624,428,127,67,627,626,429,128,68,623,622,427,126,65,1,207,424,123,63,619,618,425,124,64,621,620,426,125,699,700,697,694,304,612,502,466,370,305,613,503,467,371,306,614,468,504,372,307,615,505,469,373,308,616,506,470,374,309,617,507,471,375,310,610,500,464,368,311,611,501,465,369,312,609,499,463,367,313,606,496,460,364,314,607,497,461,365,315,608,498,462,366,684,681,674,679,86,137,213,545,442,84,135,211,546,443,85,136,547,212,444,82,140,209,548,445,83,138,210,549,446,81,139,208,550,447,77,143,219,543,440,75,141,217,544,441,76,142,218,542,439,80,146,215,539,436,78,144,216,540,437,79,145,214,541,438,680,683,677,682,153,275,296,290,25,154,276,297,291,26,155,274,289,295,24,156,278,292,286,21,157,279,293,287,22,158,277,294,288,23,151,273,302,281,31,152,271,303,282,32,150,272,301,280,30,147,269,298,284,27,148,270,299,285,28,149,268,300,283,29,686,690,692,691 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#e3fb677801a83abf4523d8c5dab7d3c82647015c862300302a3edde7221f68e9, 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 21:17:53 · history