Equation 677 Database

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Magma 1a5a7e9b1af0…

magma 1a5a7e9b1af0
Size
705
Isomorphism class hash
1a5a7e9b1af0ec5e91054518b3be38f607d0953819c97963a17dc0e784964bb8
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 20:39:27
Display reorder
660,567,328,592,587,563,329,568,593,585,561,569,327,586,591,562,324,566,588,583,559,325,564,589,584,560,326,565,590,582,558,573,334,598,578,554,574,335,599,576,552,575,333,597,577,553,330,572,594,581,557,331,570,595,579,555,332,571,596,580,556,687,688,686,685,145,273,241,380,133,274,146,242,378,134,144,275,379,240,132,272,148,244,383,136,270,149,245,381,137,271,147,243,382,135,151,264,247,375,139,152,265,248,376,140,150,266,246,377,138,267,154,250,374,142,268,155,251,372,143,269,153,249,373,141,703,704,701,702,62,322,547,83,49,323,60,548,81,50,61,321,82,546,48,318,65,550,79,52,319,63,551,80,53,320,64,549,78,51,68,313,545,74,55,66,314,543,72,56,67,312,544,73,54,316,71,541,77,58,317,69,542,75,59,315,70,540,76,57,671,672,670,669,47,162,401,391,37,163,12,399,392,35,13,164,390,400,36,165,14,397,394,40,166,15,398,395,38,167,16,396,393,39,17,160,407,389,43,18,161,405,387,41,19,159,406,388,42,156,20,403,385,46,157,21,404,386,44,158,22,402,384,45,679,680,678,677,422,171,448,442,409,172,420,449,443,410,421,173,441,447,408,170,425,444,438,412,168,423,445,439,413,169,424,446,440,411,428,177,454,433,415,426,178,455,434,416,427,179,453,432,414,176,431,450,436,418,174,429,451,437,419,175,430,452,435,417,692,691,690,689,183,290,208,202,510,288,184,209,203,511,185,289,201,207,512,293,182,204,198,513,291,180,205,199,514,292,181,206,200,515,189,296,214,193,508,190,294,215,194,509,191,295,213,192,507,299,188,210,196,504,297,186,211,197,505,298,187,212,195,506,699,700,698,697,90,125,119,98,28,123,91,117,96,26,92,124,97,118,27,121,93,115,101,24,122,94,116,99,25,120,95,114,100,23,88,131,110,104,34,89,129,108,102,32,87,130,109,103,33,127,84,113,107,30,128,85,111,105,31,126,86,112,106,29,663,664,662,661,626,217,608,347,613,218,624,606,345,614,625,216,346,607,612,220,629,611,343,616,221,627,609,344,617,219,628,610,342,615,632,223,603,338,619,630,224,604,336,620,631,222,605,337,618,226,635,602,341,622,227,633,600,339,623,225,634,601,340,621,682,683,684,681,651,309,649,648,650,310,655,653,652,654,659,311,656,657,658,308,647,644,645,646,306,638,637,636,639,307,643,641,640,642,535,300,522,520,529,536,301,523,521,530,534,302,524,519,528,303,538,525,516,532,304,539,526,517,533,305,537,527,518,531,695,696,693,694,496,8,468,462,490,6,497,469,463,491,495,7,464,470,489,11,492,471,465,486,9,493,472,466,487,10,494,473,467,488,502,3,474,460,481,503,4,475,461,482,501,5,476,459,480,2,498,477,456,484,1,499,478,457,485,0,500,479,458,483,667,668,665,666,286,261,356,236,362,262,287,354,234,360,285,263,235,355,361,260,282,359,239,365,258,283,357,237,363,259,284,358,238,364,277,252,351,231,368,278,253,352,232,366,276,254,353,233,367,255,280,350,230,371,256,281,348,228,369,257,279,349,229,370,675,676,673,674 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#c93f531644bb5fd38eabd6a6f62492ff6d9a38e5937df79a955f96fa67b29b12, 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 20:39:28 · history