Equation 677 Database

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Magma d810cd4f524a…

magma d810cd4f524a
Size
705
Isomorphism class hash
d810cd4f524aed0f5245aeb38e244860d0da130d7c7fa3ba0796881f4627b295
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 21:15:44
Display reorder
660,87,510,505,511,504,88,524,530,525,531,490,484,89,485,491,86,430,425,421,431,84,452,448,449,453,85,470,464,465,471,93,630,624,625,631,94,650,644,645,651,95,610,604,605,611,550,92,544,545,551,570,90,564,565,571,590,91,584,585,591,694,699,688,686,37,515,509,503,513,38,533,535,529,523,495,493,36,489,483,40,435,433,429,424,41,459,458,456,445,39,475,473,469,463,43,635,633,629,623,44,655,653,649,643,42,615,613,609,603,555,46,553,549,543,575,47,573,569,563,595,45,593,589,583,687,689,695,691,230,302,362,410,338,231,339,303,363,411,301,337,232,361,409,229,298,334,358,406,227,299,335,359,407,228,300,336,360,408,236,308,344,368,416,237,309,345,369,417,238,307,343,367,415,304,235,340,364,412,305,233,341,365,413,306,234,342,366,414,670,677,664,666,82,311,290,326,386,83,387,312,291,327,310,385,81,289,325,78,314,382,286,322,79,315,383,287,323,80,313,384,288,324,73,317,392,296,332,74,318,393,297,333,72,316,391,295,331,320,76,388,292,328,321,77,389,293,329,319,75,390,294,330,663,665,667,673,25,516,500,514,502,26,522,536,521,534,496,482,24,480,494,28,436,423,420,434,29,447,444,443,446,27,476,462,461,474,31,636,622,620,634,32,656,642,641,654,30,616,602,600,614,556,34,542,540,554,576,35,562,560,574,596,33,582,581,594,700,703,698,702,54,518,519,508,517,55,537,538,539,528,498,497,56,499,488,57,438,437,439,428,58,441,440,442,451,59,477,478,479,468,52,637,638,639,628,53,658,657,659,648,51,617,618,619,608,558,48,557,559,548,578,49,577,579,568,597,50,598,599,588,701,685,697,692,160,512,507,506,501,161,520,532,527,526,492,481,159,487,486,156,432,422,427,426,157,457,454,455,450,158,472,460,467,466,166,632,621,627,626,167,652,640,647,646,165,612,601,607,606,552,162,541,547,546,572,163,561,567,566,592,164,580,587,586,696,704,690,693,19,250,265,253,278,20,279,248,266,254,249,277,18,267,252,22,246,274,264,256,23,247,275,262,257,21,245,276,263,255,17,241,284,271,251,15,239,285,272,419,16,240,283,273,258,244,13,280,270,259,242,14,281,268,260,243,12,282,269,261,681,679,672,661,69,202,218,204,184,70,182,200,219,205,201,183,71,220,203,68,198,180,217,207,66,199,181,215,208,67,197,179,216,206,60,193,190,224,210,61,191,188,225,211,62,192,189,226,209,196,63,186,223,213,194,64,187,221,214,195,65,185,222,212,668,675,684,680,139,350,108,102,398,140,399,351,109,103,349,397,138,110,104,142,346,394,111,105,143,347,395,112,106,141,348,396,113,107,137,356,404,114,100,135,357,405,115,101,136,355,403,116,99,352,133,400,117,96,353,134,401,118,97,354,132,402,119,98,683,674,669,676,154,176,3,127,374,155,375,177,4,128,178,373,153,5,126,150,175,370,2,130,151,173,371,1,131,152,174,372,0,129,145,168,380,9,125,146,418,381,10,123,144,169,379,11,124,170,148,376,8,121,171,149,377,6,122,172,147,378,7,120,662,682,678,671 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#e1d7ea9e4f81623cd84c542145d634570787dd3fe7cd09a50189ca2a47386599, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:15:45 · history