Equation 677 Database

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Magma c7daeeaab55a…

magma c7daeeaab55a
Size
705
Isomorphism class hash
c7daeeaab55a232fedb579bf65ff1bea4fc64fc3e382a788150cc9dea3a37291
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 15:55:29
Display reorder
660,387,619,379,252,29,253,617,388,380,27,251,618,389,378,28,615,248,386,382,25,249,383,616,384,26,614,250,385,381,24,258,393,610,377,35,259,394,608,375,33,257,395,609,376,34,392,254,613,373,31,390,255,611,374,32,391,256,612,372,30,687,688,686,685,191,154,444,303,438,304,155,189,445,439,302,153,190,446,440,150,306,187,447,441,307,448,151,188,442,152,305,186,449,443,301,182,145,450,436,299,180,146,451,437,300,181,144,452,435,185,297,148,453,432,183,298,149,454,433,184,296,147,455,434,703,704,701,702,246,370,227,591,600,592,371,247,228,601,590,369,245,229,599,366,594,242,226,596,595,224,367,243,597,368,593,244,225,598,589,237,361,233,606,587,238,362,234,607,588,236,360,235,605,240,585,364,232,602,241,586,365,230,603,239,584,363,231,604,671,672,670,669,134,317,122,463,163,464,318,132,120,164,462,319,133,121,162,316,466,137,125,166,467,123,314,135,167,315,465,136,124,165,461,140,308,128,161,459,138,309,126,159,460,139,310,127,160,143,457,311,131,157,141,458,312,129,158,142,456,313,130,156,679,680,678,677,507,168,497,475,485,476,169,508,495,483,474,170,509,496,484,171,478,506,493,481,479,494,172,504,482,173,477,505,492,480,473,513,174,503,491,471,514,175,501,489,472,515,176,502,490,512,469,177,499,487,510,470,178,500,488,511,468,179,498,486,692,691,690,689,42,213,336,49,572,50,214,43,337,570,48,215,44,335,571,212,52,45,332,575,53,333,210,46,573,211,51,47,334,574,55,40,204,342,567,56,41,205,343,568,54,39,206,341,569,36,58,207,338,566,37,59,208,339,564,38,57,209,340,565,699,700,698,697,86,60,81,97,111,98,61,84,82,112,96,62,85,83,113,63,100,89,80,110,101,78,64,87,108,65,99,88,79,109,103,92,66,72,117,104,90,67,73,118,102,91,68,74,119,95,106,69,75,116,93,107,70,76,114,94,105,71,77,115,663,664,662,661,626,23,270,634,402,632,21,627,271,403,633,22,628,269,404,19,637,629,266,405,635,267,20,630,406,18,636,631,268,407,640,624,14,261,400,638,625,12,262,401,639,623,13,260,399,620,643,17,264,396,621,641,15,265,397,622,642,16,263,398,682,683,684,681,659,7,658,657,656,648,8,651,650,649,652,6,655,654,653,10,353,583,351,217,645,644,11,646,647,9,352,582,350,216,356,579,5,349,221,354,580,3,347,222,355,581,4,348,223,578,359,0,345,220,576,357,2,346,218,577,358,1,344,219,695,696,693,694,545,327,533,556,521,557,328,543,531,519,555,326,544,532,520,330,552,541,529,517,553,530,331,542,518,329,554,540,528,516,562,551,325,539,527,563,549,323,537,525,561,550,324,538,526,547,558,321,535,523,548,559,322,536,524,546,560,320,534,522,667,668,665,666,415,203,287,423,273,424,201,416,288,274,425,202,414,289,272,199,422,418,286,276,420,284,200,419,277,198,421,417,285,275,429,413,194,293,279,430,411,192,294,280,431,412,193,295,278,409,428,197,292,282,410,426,195,290,283,408,427,196,291,281,675,676,673,674 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#24d4369d63c88701266d916dc6f9c75e12853e26a0a22f3b011b6cf68ccd31bb, 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 15:55:30 · history