Equation 677 Database

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Magma 884bc30246b8…

magma 884bc30246b8
Size
705
Isomorphism class hash
884bc30246b89c5efd73a3943de28b57b37ecbc064354053654a59737747e909
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 15:34:54
Display reorder
660,442,441,443,440,438,439,432,433,434,435,436,437,562,563,561,558,559,560,553,554,552,556,557,555,123,124,125,122,120,121,129,130,131,128,126,127,193,194,192,196,197,195,199,200,198,202,203,201,308,306,307,311,309,310,303,304,305,302,300,301,674,692,689,681,336,338,337,341,339,340,344,342,343,347,345,346,107,105,106,103,104,102,98,96,97,101,99,100,598,599,597,594,595,596,589,590,588,592,593,591,170,168,169,173,171,172,176,174,175,179,177,178,476,474,475,479,477,478,471,472,473,470,468,469,685,703,695,700,544,543,545,542,540,541,549,550,551,548,546,547,427,428,426,430,431,429,425,423,424,421,422,420,285,286,287,284,282,283,276,277,278,279,280,281,266,264,265,269,267,268,272,270,271,275,273,274,291,292,293,290,288,289,297,298,299,296,294,295,664,678,669,670,110,109,108,112,113,111,115,116,114,118,119,117,181,182,180,184,185,183,187,188,186,190,191,189,601,602,600,604,605,603,607,608,606,610,611,609,489,490,491,488,486,487,480,481,482,483,484,485,349,350,348,352,353,351,355,356,354,358,359,357,675,690,680,686,361,360,362,363,364,365,366,367,368,369,370,371,33,34,35,32,30,31,24,25,26,27,28,29,71,69,70,67,68,66,62,60,61,65,63,64,496,497,495,492,493,494,502,503,501,498,499,500,613,614,612,616,617,615,619,620,618,622,623,621,687,702,699,697,521,520,519,516,517,518,526,527,525,522,523,524,645,646,647,644,642,643,636,637,638,639,640,641,22,23,21,18,19,20,13,14,12,16,17,15,49,50,48,52,53,51,55,56,54,58,59,57,385,386,384,388,389,387,391,392,390,394,395,393,688,704,693,698,243,245,244,241,242,240,251,249,250,247,248,246,210,211,212,213,214,215,208,209,207,204,205,206,222,223,224,225,226,227,220,221,219,216,217,218,234,235,236,237,238,239,232,233,231,228,229,230,8,6,7,11,9,10,3,4,5,2,1,0,661,666,662,667,454,453,455,452,450,451,444,445,446,447,448,449,258,259,260,261,262,263,256,257,255,252,253,254,321,322,323,320,318,319,312,313,314,315,316,317,575,573,574,571,572,570,566,564,565,569,567,568,139,140,138,142,143,141,137,135,136,133,134,132,673,691,682,683,539,538,537,534,535,536,529,530,528,532,533,531,91,92,90,94,95,93,89,87,88,85,86,84,405,406,407,404,402,403,396,397,398,399,400,401,659,657,658,655,656,654,650,648,649,653,651,652,413,411,412,409,410,408,419,417,418,415,416,414,684,701,694,696,383,382,381,378,379,380,373,374,372,376,377,375,44,42,43,47,45,46,39,40,41,38,36,37,72,73,74,75,76,77,78,79,80,81,82,83,630,631,632,633,634,635,628,629,627,624,625,626,505,506,504,508,509,507,511,512,510,514,515,513,663,677,668,672,328,327,329,326,324,325,333,334,335,332,330,331,153,154,155,152,150,151,144,145,146,147,148,149,576,577,578,579,580,581,582,583,584,585,586,587,160,161,159,156,157,158,166,167,165,162,163,164,467,465,466,463,464,462,458,456,457,461,459,460,665,679,676,671 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {61} 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 15:34:55 · history