Equation 677 Database

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Magma 6706303a8761…

magma 6706303a8761
Size
705
Isomorphism class hash
6706303a87614af2b63b97fc9b3d559b17285c5e51a81de47c79ecadc53360f8
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 19:12:24
Display reorder
660,490,470,77,434,562,491,75,435,563,471,489,469,76,433,561,466,486,73,430,558,467,487,74,431,559,468,488,72,432,560,83,461,481,425,553,81,462,482,426,554,82,460,480,424,552,464,79,484,428,556,465,80,485,429,557,427,463,78,483,555,681,680,686,677,300,422,27,315,246,298,28,313,244,423,299,421,29,314,245,418,303,26,311,249,419,301,24,312,247,420,302,25,310,248,33,413,295,306,252,34,414,296,304,250,35,412,297,305,251,416,32,294,309,255,417,30,292,307,253,308,415,31,293,254,668,663,665,672,410,514,265,326,538,411,266,327,539,515,409,513,267,325,537,510,406,264,322,534,511,407,262,323,535,512,408,263,324,536,256,505,401,317,529,257,506,402,318,530,258,504,400,316,528,508,259,404,320,532,509,260,405,321,533,319,507,261,403,531,676,683,684,673,650,646,20,648,647,658,18,656,655,654,642,638,19,640,639,614,618,23,616,615,622,626,21,624,623,630,634,22,632,631,15,226,565,473,229,16,224,566,474,230,17,225,564,472,231,598,14,599,601,600,606,12,610,608,607,475,227,13,567,228,704,698,703,697,151,165,0,155,338,149,2,156,339,166,150,164,1,157,337,168,147,4,154,334,169,148,5,152,335,167,146,3,153,336,7,171,142,161,329,8,172,140,162,330,6,170,141,163,328,174,10,145,160,332,175,11,143,158,333,159,173,9,144,331,691,693,690,689,550,526,197,216,211,551,198,217,209,527,549,525,199,215,210,522,546,196,212,207,523,547,194,213,208,524,548,195,214,206,188,517,541,222,202,189,518,542,223,200,190,516,540,221,201,520,191,544,218,205,521,192,545,219,203,220,519,193,543,204,669,667,661,664,107,56,120,111,92,105,121,112,90,54,106,55,122,113,91,59,103,123,110,95,57,104,124,108,93,58,102,125,109,94,126,51,98,117,87,127,52,96,118,88,128,53,97,119,89,50,129,101,116,86,48,130,99,114,84,115,49,131,100,85,695,692,696,694,582,594,63,446,502,583,64,447,503,595,581,593,65,445,501,590,578,62,442,498,591,579,60,443,499,592,580,61,444,500,69,585,573,437,493,70,586,574,438,494,71,584,572,436,492,588,68,576,440,496,589,66,577,441,497,439,587,67,575,495,687,688,682,678,649,651,40,644,645,657,41,652,653,659,641,643,39,636,637,619,617,36,612,613,627,625,37,620,621,635,633,38,629,628,46,569,479,135,137,47,570,477,133,138,45,568,478,134,136,603,42,602,597,596,611,43,609,605,604,132,571,44,476,139,699,701,702,700,277,385,241,291,398,278,242,289,399,386,279,387,243,290,397,384,276,240,287,394,382,274,238,288,395,383,275,239,286,396,232,376,268,282,389,233,377,269,280,390,234,378,270,281,388,379,235,271,285,392,380,236,272,283,393,284,381,237,273,391,671,670,662,666,458,361,187,345,374,459,185,343,375,362,457,363,186,344,373,360,454,183,341,370,358,455,184,342,371,359,456,182,340,372,178,352,449,351,365,176,353,450,349,366,177,354,448,350,364,355,181,452,347,368,356,179,453,348,369,346,357,180,451,367,679,674,675,685 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#9017e525a3aedea68e654a603b277c6c50731afc33f3d9497441ab6abb8d2314, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:12:25 · history