Equation 677 Database

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Magma a61c19c1c002…

magma a61c19c1c002
Size
705
Isomorphism class hash
a61c19c1c002fa08b1f0a0be9c3de4dac3f4946d66c1f7e513430595ffed4361
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 18:15:30
Display reorder
660,303,38,327,339,315,328,36,340,316,304,37,305,329,341,317,302,34,326,338,314,300,35,324,336,312,301,33,325,337,313,44,294,318,330,306,42,295,319,331,307,43,296,320,332,308,297,40,321,333,309,298,41,322,334,310,335,299,39,323,311,685,686,688,687,427,186,459,417,442,460,187,418,443,428,185,426,461,419,441,430,182,458,416,438,431,183,456,414,439,429,184,457,415,440,192,433,450,423,448,193,434,451,424,449,191,432,452,425,447,436,188,453,422,444,437,189,454,420,445,421,435,190,455,446,701,702,704,703,548,293,572,589,567,573,291,590,565,549,292,547,571,591,566,544,289,568,588,563,545,290,569,586,564,546,288,570,587,562,284,554,578,580,558,282,555,579,581,556,283,553,577,582,557,550,287,574,583,561,551,285,575,584,559,585,552,286,576,560,670,669,672,671,476,6,207,468,197,208,7,469,198,474,8,475,206,470,199,479,9,210,471,196,477,10,211,472,194,478,11,209,473,195,4,482,213,466,203,5,480,214,467,204,3,481,212,465,205,485,1,216,462,202,483,0,217,463,200,464,484,2,215,201,680,677,679,678,125,497,225,118,46,226,495,116,47,126,496,127,224,117,45,124,493,228,121,49,122,494,229,119,50,123,492,227,120,48,488,131,223,113,52,486,132,221,114,53,487,133,222,115,51,130,491,219,112,55,128,489,220,110,56,111,129,490,218,54,689,690,691,692,61,256,151,105,530,149,254,106,528,62,255,60,150,104,529,57,259,147,108,533,58,257,148,109,531,59,258,146,107,532,262,67,157,103,525,260,68,155,101,526,261,66,156,102,527,63,265,153,99,524,64,263,154,100,522,98,65,264,152,523,697,698,700,699,627,603,651,608,632,649,601,609,633,625,602,626,650,607,631,623,599,647,604,628,624,600,648,605,629,622,598,646,606,630,594,618,642,614,638,592,616,640,615,639,593,617,641,613,637,621,597,645,610,634,619,595,643,611,635,612,620,596,644,636,661,662,664,663,355,166,380,345,369,378,164,346,370,356,165,354,379,347,371,358,169,383,344,368,359,167,381,342,366,357,168,382,343,367,161,361,386,351,375,162,362,384,352,376,163,360,385,353,377,364,160,389,350,374,365,158,387,348,372,349,363,159,388,373,682,681,684,683,278,83,539,269,17,540,84,270,15,276,85,277,538,271,16,281,82,542,268,20,279,80,543,266,18,280,81,541,267,19,74,656,659,658,657,75,69,537,275,73,76,653,654,652,655,72,77,535,274,14,70,78,536,272,12,273,71,79,534,13,693,694,696,695,242,138,512,236,504,510,139,237,505,243,137,244,511,238,506,245,134,515,239,507,246,135,513,240,508,247,136,514,241,509,144,248,518,234,502,145,249,516,235,503,143,250,517,233,501,251,140,521,230,498,252,141,519,231,499,232,253,142,520,500,666,665,668,667,402,179,29,396,89,27,180,397,90,403,181,404,28,398,91,405,178,32,399,88,406,176,30,400,86,407,177,31,401,87,170,408,24,394,95,171,409,25,395,96,172,410,26,393,97,411,173,23,390,94,412,174,21,391,92,392,413,175,22,93,674,673,676,675 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#70fbce4d1be954c5232f18b8807a18e39f88f6f161a168e0f82db887a05a7819, 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 18:15:32 · history