Equation 677 Database

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Magma 10d956be7b53…

magma 10d956be7b53
Size
705
Isomorphism class hash
10d956be7b5385c49a57e7f0c0f0c1184719004146bb70523e458606089ad2d3
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 19:56:14
Display reorder
660,381,127,465,518,441,379,125,463,516,439,380,126,464,517,440,130,377,461,514,437,128,378,462,515,438,129,376,460,513,436,372,133,456,509,432,370,131,454,507,430,371,132,455,508,431,136,375,459,512,435,134,373,457,510,433,135,374,458,511,434,682,677,675,679,494,79,364,299,316,492,77,362,300,314,493,78,363,301,315,82,490,360,302,312,80,491,361,303,313,81,489,359,304,311,485,85,355,297,307,483,83,353,298,305,484,84,354,296,306,88,488,358,293,310,86,486,356,294,308,87,487,357,295,309,671,662,666,663,352,193,200,547,571,350,191,201,545,569,351,192,202,546,570,196,348,199,543,567,194,349,197,544,568,195,347,198,542,566,343,188,206,538,562,341,189,207,536,560,342,190,208,537,561,187,346,205,541,565,185,344,203,539,563,186,345,204,540,564,684,685,673,686,656,119,653,655,659,640,120,636,639,643,648,121,644,647,651,122,624,620,623,627,123,632,629,631,635,124,616,612,615,619,288,117,282,286,521,289,118,280,284,519,290,116,281,285,520,113,606,605,608,609,114,291,279,287,522,115,292,1,283,523,697,699,703,704,173,238,336,393,162,174,236,337,391,163,175,237,335,392,161,234,176,339,389,165,235,177,340,390,166,233,178,338,388,164,179,244,334,384,168,180,242,332,382,169,181,243,333,383,167,240,182,330,387,171,241,183,331,385,172,239,184,329,386,170,693,689,692,691,583,9,100,429,559,581,7,98,427,557,582,8,99,428,558,12,579,96,425,555,10,580,97,426,556,11,578,95,424,554,574,4,91,420,550,572,5,89,418,548,573,6,90,419,549,3,577,94,423,553,0,575,92,421,551,2,576,93,422,552,664,670,672,661,254,66,267,602,603,255,67,268,599,598,256,68,266,600,601,65,253,263,69,26,63,251,264,597,596,64,252,265,76,25,245,57,258,72,30,246,58,259,70,31,247,59,257,71,32,60,248,261,75,29,61,249,262,73,27,62,250,260,74,28,696,695,694,690,453,17,595,400,417,451,18,593,401,415,452,16,594,402,416,13,449,591,403,413,14,450,592,404,414,15,448,590,405,412,444,23,586,398,408,442,24,584,399,406,443,22,585,397,407,19,447,589,394,411,20,445,587,395,409,21,446,588,396,410,683,676,678,687,658,157,652,654,657,642,155,637,638,641,650,156,645,646,649,160,626,621,622,625,158,634,628,630,633,159,618,613,614,617,480,152,271,276,369,478,153,272,274,367,479,154,273,275,368,151,611,610,604,607,149,481,270,277,366,150,482,269,278,365,700,698,702,701,38,231,535,321,104,36,232,533,322,105,37,230,534,320,106,227,34,531,317,103,228,35,532,318,101,229,33,530,319,102,44,222,526,327,110,42,223,524,328,111,43,221,525,326,112,225,40,529,323,109,226,41,527,324,107,224,39,528,325,108,665,669,667,668,54,211,506,137,477,56,209,504,138,475,52,210,505,139,476,214,46,502,140,473,212,47,503,141,474,213,49,501,142,472,51,217,497,143,468,53,215,495,144,466,55,216,496,145,467,220,50,500,146,471,218,45,498,147,469,219,48,499,148,470,674,680,688,681 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#b42b2593cdf495fd739236f86f5dbe699df6ba394eb7d6a8f934bf0cd7c90649, 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 19:56:15 · history