Equation 677 Database

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Magma bd6d35b931c4…

magma bd6d35b931c4
Size
705
Isomorphism class hash
bd6d35b931c4e9286e2b27f14b199764db916d1e48e7b4cf21f3fad2862a8c40
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 20:45:18
Display reorder
660,419,395,505,44,457,420,396,506,42,458,418,394,504,43,456,422,398,508,47,460,423,399,509,45,461,421,397,507,46,459,417,393,39,503,455,415,391,40,501,453,416,392,41,502,454,389,413,38,499,451,390,414,36,500,452,388,412,37,498,450,683,680,676,678,3,178,215,127,194,4,179,216,128,195,5,180,214,126,193,2,181,218,123,190,1,182,219,124,191,0,183,217,125,192,9,176,133,213,185,10,177,134,211,186,11,175,132,212,184,172,8,129,209,188,173,6,130,210,189,174,7,131,208,187,665,672,667,668,481,555,371,221,143,482,556,372,222,141,480,554,370,220,142,484,558,374,224,146,485,559,375,225,144,483,557,373,223,145,479,553,227,369,138,477,551,228,367,139,478,552,226,368,140,549,475,230,365,137,550,476,231,366,135,548,474,229,364,136,675,674,687,681,620,624,621,29,623,629,632,628,27,631,612,616,613,28,615,644,648,645,25,647,652,656,653,26,655,636,640,637,24,639,605,608,35,606,607,589,592,33,590,591,597,600,34,598,599,574,572,31,576,577,584,581,32,580,583,448,122,30,121,159,704,702,697,703,347,100,359,254,21,348,101,360,255,22,346,99,358,253,23,350,96,362,250,20,351,97,363,251,18,349,98,361,252,19,345,106,245,357,12,343,107,246,355,13,344,105,244,356,14,102,341,248,353,15,103,342,249,354,16,104,340,247,352,17,691,692,694,690,469,407,543,153,383,470,408,544,154,384,468,406,542,155,382,472,410,546,156,386,473,411,547,157,387,471,409,545,158,385,467,405,151,541,381,465,403,152,539,379,466,404,150,540,380,401,463,147,537,377,402,464,148,538,378,400,462,149,536,376,671,662,663,666,289,294,518,109,61,290,292,519,110,62,291,293,517,108,60,288,297,521,112,64,286,295,522,113,65,287,296,520,111,63,280,300,115,516,67,281,298,116,514,68,282,299,114,515,66,303,283,118,512,70,301,284,119,513,71,302,285,117,511,69,693,695,696,689,311,443,493,237,567,312,444,494,235,568,310,442,492,236,566,314,446,496,233,570,315,447,497,234,571,313,445,495,232,569,309,441,243,491,565,307,439,241,489,563,308,440,242,490,564,437,305,239,487,561,438,306,240,488,562,436,304,238,486,560,682,688,679,673,627,626,625,80,622,635,634,633,78,630,619,618,617,79,614,651,650,649,83,646,659,658,657,81,654,643,642,641,82,638,611,610,75,609,604,595,594,76,593,588,603,602,77,601,596,578,579,74,575,573,586,587,72,585,582,510,535,73,449,120,699,700,701,698,320,331,431,161,199,321,332,432,162,200,319,333,430,160,201,316,330,434,164,198,317,328,435,165,196,318,329,433,163,197,326,337,167,429,205,327,338,168,427,206,325,339,166,428,207,336,322,170,425,204,334,323,171,426,202,335,324,169,424,203,664,661,669,670,91,262,530,49,279,92,263,531,50,277,90,264,529,48,278,94,265,533,52,275,95,266,534,53,276,93,267,532,51,274,89,260,55,528,270,87,261,56,526,268,88,259,54,527,269,256,85,58,524,273,257,86,59,525,271,258,84,57,523,272,684,686,677,685 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#d33e4a3e2f8aecd7db8c3ccbf48af948a122b54aec333d772566c797fe9ef74b, 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 20:45:19 · history