Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 5044ced10784…

magma 5044ced10784
Size
705
Isomorphism class hash
5044ced1078406a7f5cf9e4263b60f1a98bf46fea87e90685bcf77d3b8ae2a13
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 17:22:18
Display reorder
660,301,133,144,311,18,302,134,142,312,16,303,135,143,310,17,136,304,140,307,14,137,305,308,15,141,309,138,306,139,13,299,131,150,317,9,300,132,148,318,7,298,130,149,316,8,127,295,146,313,12,128,296,147,314,10,129,297,145,315,11,685,686,688,687,200,66,361,51,197,201,64,362,49,198,199,65,363,50,196,62,203,364,54,193,63,204,52,194,365,53,61,202,366,195,206,57,359,46,188,207,55,360,47,189,205,56,358,48,187,60,209,355,45,191,58,210,356,43,192,59,208,357,44,190,701,702,704,703,29,123,274,574,294,30,121,275,575,292,28,122,276,576,293,126,25,273,577,290,124,26,578,291,271,579,125,27,272,289,20,118,280,572,285,21,119,281,573,283,19,120,282,571,284,117,23,279,568,288,115,24,277,569,286,116,22,278,570,287,670,669,672,671,382,216,404,401,371,383,214,405,402,372,384,215,403,400,370,212,381,407,397,367,213,379,398,368,408,399,211,380,406,369,388,222,410,392,377,389,220,411,393,378,390,221,409,391,376,218,387,413,395,373,219,385,414,396,374,217,386,412,394,375,680,677,679,678,226,35,430,421,448,227,36,431,422,449,228,34,432,423,450,31,225,429,424,447,32,223,425,445,427,426,33,224,428,446,232,41,436,419,439,233,42,437,420,440,234,40,438,418,441,37,231,435,415,442,38,229,433,416,443,39,230,434,417,444,689,690,691,692,523,255,507,546,521,524,253,505,544,522,525,254,506,545,520,258,526,510,542,517,256,527,543,518,508,541,257,528,509,519,529,250,502,537,512,530,251,503,535,513,531,252,504,536,511,249,532,501,540,515,247,533,499,538,516,248,534,500,539,514,697,698,700,699,608,584,639,619,596,609,585,637,620,597,607,583,638,621,595,580,604,635,618,592,581,605,616,593,636,617,582,606,634,594,614,590,630,625,602,615,591,628,626,603,613,589,629,627,601,586,610,633,624,598,587,611,631,622,599,588,612,632,623,600,661,662,664,663,174,90,334,325,159,172,88,335,326,157,173,89,336,327,158,86,170,333,328,162,87,171,329,160,331,330,85,169,332,161,165,81,340,323,154,163,79,341,324,155,164,80,342,322,156,84,168,339,319,153,82,166,337,320,151,83,167,338,321,152,682,681,684,683,559,262,550,563,0,560,263,551,561,2,558,264,552,562,3,261,555,549,566,4,259,556,564,5,547,565,260,557,548,6,646,268,645,647,644,554,269,553,567,1,641,270,640,642,643,267,658,656,659,657,265,650,648,651,649,266,654,652,655,653,693,694,696,695,468,240,491,480,456,466,238,492,478,454,467,239,490,479,455,236,464,487,476,452,237,465,477,453,488,475,235,463,489,451,474,246,497,486,462,472,244,498,484,460,473,245,496,485,461,242,470,493,482,458,243,471,494,483,459,241,469,495,481,457,666,665,668,667,108,344,75,182,97,106,345,73,183,98,107,343,74,181,99,347,104,78,185,100,348,105,186,101,76,184,346,103,77,102,114,350,70,180,95,112,351,71,178,96,113,349,72,179,94,353,110,69,176,91,354,111,67,177,92,352,109,68,175,93,674,673,676,675 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#514dffc0e0e0286a01e02cffb6912c439b28b51da818e57a2690264fae383974, 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 17:22:19 · history