Equation 677 Database

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Magma b276eb040a1c…

magma b276eb040a1c
Size
705
Isomorphism class hash
b276eb040a1cac7ed3b9e330d6690395b07b41a438e3040e35af3c768a9114dc
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 17:44:11
Display reorder
660,399,594,606,617,582,397,592,604,618,580,398,593,605,616,581,597,402,609,620,585,595,400,607,621,583,596,401,608,619,584,405,600,612,623,588,403,598,610,624,586,404,599,611,622,587,603,408,615,626,591,601,406,613,627,589,602,407,614,625,590,687,688,686,685,447,288,300,312,268,445,286,298,310,269,446,287,299,311,270,284,450,296,308,267,285,448,297,309,265,283,449,295,307,266,453,279,291,303,274,451,277,289,301,275,452,278,290,302,276,282,456,294,306,273,280,454,292,304,271,281,455,293,305,272,703,704,701,702,161,377,388,60,576,162,378,389,58,574,160,376,390,59,575,373,157,387,56,579,374,158,385,57,577,375,159,386,55,578,167,383,394,51,571,168,384,395,49,572,166,382,396,50,573,379,163,393,54,570,380,164,391,52,568,381,165,392,53,569,671,672,670,669,314,133,465,120,130,315,134,463,118,131,313,135,464,119,132,136,317,468,116,129,137,318,466,117,127,138,316,467,115,128,320,139,460,111,121,321,140,461,109,122,319,141,462,110,123,142,323,459,114,124,143,324,457,112,125,144,322,458,113,126,679,680,678,677,5,504,514,476,484,6,502,515,477,485,4,503,516,475,486,500,0,513,479,483,501,2,511,480,481,499,3,512,478,482,11,495,505,474,490,12,493,506,472,491,10,494,507,473,492,498,7,508,470,489,496,8,509,471,487,497,9,510,469,488,692,691,690,689,42,185,197,153,535,40,186,198,151,536,41,184,196,152,537,181,38,193,156,538,182,39,194,154,539,183,37,195,155,540,48,191,203,148,533,46,192,204,149,534,47,190,202,150,532,187,44,199,147,529,188,45,200,145,530,189,43,201,146,531,699,700,698,697,24,85,34,67,82,22,86,35,68,83,23,87,36,69,84,88,20,33,70,81,89,21,31,71,79,90,19,32,72,80,15,91,25,65,73,13,92,26,66,74,14,93,27,64,75,94,18,28,61,76,95,16,29,62,77,96,17,30,63,78,663,664,662,661,630,209,221,234,415,628,210,222,232,416,629,208,220,233,417,205,633,217,230,418,206,631,218,231,419,207,632,219,229,420,636,215,227,240,413,634,216,228,238,414,635,214,226,239,412,211,639,223,236,409,212,637,224,237,410,213,638,225,235,411,682,683,684,681,107,654,655,653,652,108,658,659,657,656,106,650,651,649,648,1,103,561,554,553,641,104,642,640,643,644,105,647,646,645,98,560,563,544,548,99,558,564,545,549,97,559,562,546,547,556,101,566,543,551,557,102,567,541,552,555,100,565,542,550,695,696,693,694,521,353,364,329,341,522,354,365,330,342,520,352,366,328,340,349,517,363,325,337,350,518,361,326,338,351,519,362,327,339,527,359,370,335,347,528,360,371,336,348,526,358,372,334,346,355,523,369,331,343,356,524,367,332,344,357,525,368,333,345,667,668,665,666,175,428,438,252,263,176,429,436,250,264,177,427,437,251,262,431,178,434,248,259,432,179,435,249,260,430,180,433,247,261,173,426,444,243,254,174,424,442,241,255,172,425,443,242,253,422,169,440,246,257,423,170,441,244,258,421,171,439,245,256,675,676,673,674 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#61e4460e7132ae46985bdc51b44ba41f1d8967bba1a2e054d2c046422600ec54, 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 17:44:12 · history