Equation 677 Database

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Magma 183c9d8aa07b…

magma 183c9d8aa07b
Size
705
Isomorphism class hash
183c9d8aa07baeb277e313ca337c918fb150314cc8a1d5ff3b0d750037499649
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 18:09:37
Display reorder
660,119,589,107,244,229,117,590,105,245,230,118,588,106,243,228,122,592,240,232,110,120,593,108,241,233,121,591,109,242,231,113,125,235,595,227,111,123,236,596,225,112,124,234,594,226,128,116,238,598,223,126,114,239,599,224,597,127,115,237,222,687,688,686,685,400,360,389,420,410,401,361,387,421,408,399,362,388,422,409,396,363,423,413,385,397,364,386,424,411,398,365,384,425,412,395,406,426,366,416,393,407,427,367,414,394,405,428,368,415,402,391,429,369,419,403,392,430,370,417,371,404,390,431,418,703,704,701,702,316,583,311,337,326,317,584,309,338,324,315,582,310,336,325,312,586,340,329,307,313,587,308,341,327,314,585,306,339,328,302,322,343,581,332,300,323,344,579,330,301,321,342,580,331,318,305,346,577,335,319,303,347,578,333,576,320,304,345,334,671,672,670,669,439,197,32,19,88,440,195,30,20,89,438,196,31,18,87,442,193,15,91,28,443,194,29,16,92,441,192,27,17,90,23,437,10,188,86,21,435,11,186,84,22,436,9,187,85,433,26,13,191,82,434,24,14,189,83,190,432,25,12,81,679,680,678,677,450,93,214,209,459,451,94,215,207,460,452,95,213,208,461,453,96,205,458,210,454,97,211,206,456,455,98,212,204,457,220,448,200,99,465,221,449,198,100,466,219,447,199,101,467,444,216,203,102,464,445,217,201,103,462,104,446,218,202,463,692,691,690,689,529,278,518,552,542,530,276,516,553,540,528,277,517,554,541,532,281,555,545,521,533,279,519,556,543,531,280,520,557,544,524,535,558,273,548,522,536,559,274,546,523,534,560,275,547,538,527,561,272,551,539,525,562,270,549,271,537,526,563,550,699,700,698,697,146,62,135,168,158,144,60,136,169,156,145,61,137,170,157,142,58,167,154,138,143,59,139,165,155,141,57,140,166,153,133,152,174,68,164,134,150,175,66,162,132,151,176,67,163,148,129,173,64,160,149,130,171,65,161,63,147,131,172,159,663,664,662,661,601,250,638,626,614,602,251,636,624,612,600,249,637,625,613,604,246,629,617,641,605,247,639,627,615,603,248,640,628,616,644,607,632,256,620,642,608,630,257,618,643,606,631,255,619,610,647,635,252,623,611,645,633,253,621,254,609,646,634,622,682,683,684,681,291,568,288,6,178,292,569,289,7,179,293,567,290,8,177,659,564,658,657,656,650,565,649,648,651,655,566,654,652,653,286,297,4,574,181,287,298,5,575,182,285,299,3,573,180,296,282,1,570,184,294,283,0,571,185,572,295,284,2,183,695,696,693,694,494,35,484,479,504,492,33,485,477,505,493,34,483,478,506,497,38,475,507,480,495,36,481,476,508,496,37,482,474,509,490,500,470,41,510,491,498,468,39,511,489,499,469,40,512,503,486,473,44,513,501,487,471,42,514,43,502,488,472,515,667,668,665,666,261,72,348,380,54,262,73,349,378,55,263,74,350,379,56,260,71,383,53,351,258,69,352,381,51,259,70,353,382,52,354,267,375,78,45,355,268,376,79,46,356,269,377,80,47,266,357,374,77,48,264,358,372,75,49,76,265,359,373,50,675,676,673,674 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#676093fc8b0a9c703c9b4a913f63a03a075a7ec27635c2c42c5b015ba025ae64, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 18:09:38 · history