Equation 677 Database

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Magma 881d08f1184b…

magma 881d08f1184b
Size
705
Isomorphism class hash
881d08f1184b8fdb682dc49272ff0d36aa664c5bcde561b13491568b922c9594
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 18:45:51
Display reorder
660,283,12,269,290,299,267,13,288,297,284,268,14,282,289,298,11,272,279,286,302,9,270,280,287,300,10,271,281,285,301,18,274,296,264,305,275,19,294,265,303,20,273,295,266,304,277,17,292,263,308,278,15,293,261,306,276,16,291,262,307,685,686,688,687,161,413,52,117,99,53,411,118,100,159,51,412,160,119,101,416,55,164,120,102,414,56,162,121,103,415,54,163,122,104,408,156,123,50,97,157,409,124,48,98,410,158,125,49,96,155,407,126,46,93,153,405,127,47,94,154,406,128,45,95,701,702,704,703,578,249,569,542,561,567,250,540,562,576,568,251,577,541,563,252,565,581,545,560,253,566,579,543,558,254,564,580,544,559,255,584,548,575,552,582,256,546,573,553,257,583,547,574,554,587,258,551,571,555,585,259,549,572,556,586,260,550,570,557,670,669,672,671,59,422,143,171,136,141,420,172,137,57,142,421,58,173,135,418,146,62,174,139,419,144,60,175,140,417,145,61,176,138,428,65,169,149,134,63,426,170,147,132,427,64,168,148,133,68,424,165,152,130,66,425,166,150,131,67,423,167,151,129,680,677,679,678,431,78,469,451,456,470,79,452,457,429,468,80,430,450,458,77,465,434,447,455,75,466,432,448,453,76,467,433,449,454,69,437,442,475,462,435,70,443,476,463,71,436,441,474,464,440,72,445,471,461,438,73,446,472,459,439,74,444,473,460,689,690,691,692,218,506,210,225,197,211,504,226,195,216,212,505,217,227,196,502,209,214,228,200,503,207,215,229,198,501,208,213,230,199,512,224,231,201,192,222,510,232,202,193,511,223,233,203,194,220,508,234,204,191,221,509,235,205,189,219,507,236,206,190,697,698,700,699,600,588,647,612,626,645,589,613,624,601,646,590,602,614,625,591,643,603,615,629,592,644,604,616,627,593,642,605,617,628,594,606,618,638,632,607,595,619,636,630,596,608,620,637,631,609,597,621,641,635,610,598,622,639,633,611,599,623,640,634,661,662,664,663,338,86,324,347,312,325,84,345,313,336,326,85,337,346,314,82,323,334,350,311,83,321,335,348,309,81,322,333,349,310,92,344,353,330,318,342,90,351,331,319,91,343,352,332,320,340,88,356,329,317,341,89,354,327,315,339,87,355,328,316,682,681,684,683,5,241,538,518,527,539,242,516,525,3,537,240,4,517,526,237,534,8,521,530,238,535,6,519,528,239,536,7,520,529,247,653,652,655,654,657,248,656,659,658,246,648,649,650,651,2,243,515,532,524,1,244,513,533,522,0,245,514,531,523,693,694,696,695,34,21,180,485,498,181,22,483,499,35,182,23,33,484,500,24,179,37,488,497,25,177,38,486,495,26,178,36,487,496,27,40,480,186,489,41,28,481,187,490,29,39,482,188,491,43,30,479,185,492,44,31,477,183,493,42,32,478,184,494,666,665,668,667,364,114,396,371,391,397,115,369,392,365,398,116,363,370,390,113,395,367,374,387,111,393,368,372,388,112,394,366,373,389,105,362,377,402,382,360,106,375,403,383,107,361,376,404,381,358,108,380,401,385,359,109,378,399,386,357,110,379,400,384,674,673,676,675 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#8513f42721191fc76047535e55730c0acbdcae75cecf1dd6e4636ed6d0c5727e, 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 18:45:52 · history