Equation 677 Database

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Magma 5ed4449b6f7a…

magma 5ed4449b6f7a
Size
705
Isomorphism class hash
5ed4449b6f7a66ae4653b80e23f5621d641de7b760563b0762fb4ba80b0526c1
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 21:47:43
Display reorder
660,631,630,632,633,634,635,628,629,627,624,625,626,643,644,642,646,647,645,641,639,640,637,638,636,606,607,608,609,610,611,604,605,603,600,601,602,620,618,619,623,621,622,615,616,617,614,612,613,452,450,451,455,453,454,447,448,449,446,444,445,686,679,685,684,385,384,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,409,410,408,412,413,411,415,416,414,418,419,417,383,381,382,379,380,378,374,372,373,377,375,376,27,28,29,26,24,25,33,34,35,32,30,31,666,663,669,670,113,112,111,108,109,110,118,119,117,114,115,116,42,43,44,45,46,47,40,41,39,36,37,38,651,652,653,650,648,649,657,658,659,656,654,655,421,422,420,424,425,423,427,428,426,430,431,429,463,464,462,466,467,465,461,459,460,457,458,456,673,677,687,688,177,179,178,175,176,174,170,168,169,173,171,172,133,134,132,136,137,135,139,140,138,142,143,141,154,155,153,150,151,152,145,146,144,148,149,147,166,167,165,162,163,164,157,158,156,160,161,159,122,120,121,125,123,124,128,126,127,131,129,130,700,699,701,704,230,229,228,232,233,231,235,236,234,238,239,237,245,243,244,241,242,240,251,249,250,247,248,246,258,259,260,261,262,263,256,257,255,252,253,254,272,270,271,275,273,274,267,268,269,266,264,265,82,83,81,78,79,80,73,74,72,76,77,75,692,689,695,696,513,515,514,511,512,510,506,504,505,509,507,508,526,527,525,522,523,524,517,518,516,520,521,519,530,528,529,533,531,532,536,534,535,539,537,538,542,540,541,545,543,544,548,546,547,551,549,550,69,70,71,68,66,67,60,61,62,63,64,65,661,662,668,667,277,276,278,279,280,281,282,283,284,285,286,287,289,290,288,292,293,291,295,296,294,298,299,297,310,311,309,306,307,308,301,302,300,304,305,303,323,321,322,319,320,318,314,312,313,317,315,316,88,89,87,84,85,86,94,95,93,90,91,92,691,690,693,694,56,55,54,58,59,57,53,51,52,49,50,48,478,479,477,474,475,476,469,470,468,472,473,471,480,481,482,483,484,485,486,487,488,489,490,491,493,494,492,496,497,495,499,500,498,502,503,501,443,441,442,439,440,438,434,432,433,437,435,436,674,678,680,681,361,360,362,363,364,365,366,367,368,369,370,371,325,326,324,328,329,327,331,332,330,334,335,333,347,345,346,343,344,342,338,336,337,341,339,340,359,357,358,355,356,354,350,348,349,353,351,352,105,106,107,104,102,103,96,97,98,99,100,101,698,697,702,703,187,186,188,189,190,191,184,185,183,180,181,182,198,199,200,201,202,203,196,197,195,192,193,194,214,215,213,210,211,212,205,206,204,208,209,207,225,226,227,224,222,223,216,217,218,219,220,221,17,15,16,13,14,12,23,21,22,19,20,18,665,664,671,672,553,552,554,555,556,557,558,559,560,561,562,563,565,566,564,568,569,567,571,572,570,574,575,573,586,587,585,582,583,584,577,578,576,580,581,579,597,598,599,596,594,595,588,589,590,591,592,593,4,5,3,1,0,2,10,11,9,6,7,8,675,676,683,682 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, 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 21:47:44 · history