Equation 677 Database

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Magma 2b3da929d22f…

magma 2b3da929d22f
Size
705
Isomorphism class hash
2b3da929d22f81d8f3110d19012aea39fce28bf96441cf852edb908773c64335
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 15:57:35
Display reorder
660,7,377,256,391,370,8,375,257,392,371,6,376,255,390,369,380,10,252,387,373,378,11,253,388,374,379,9,254,389,372,5,383,247,397,368,3,381,248,398,366,4,382,246,396,367,386,0,250,393,364,384,2,251,394,365,385,1,249,395,363,685,686,688,687,173,461,116,109,454,171,459,114,110,455,172,460,115,108,453,464,169,119,112,457,462,170,117,113,458,463,168,118,111,456,164,467,122,107,452,162,465,120,105,450,163,466,121,106,451,470,167,125,103,448,468,165,123,104,449,469,166,124,102,447,701,702,704,703,351,224,44,238,584,352,222,42,239,582,353,223,43,237,583,227,354,47,234,587,225,355,45,235,585,226,356,46,236,586,357,230,39,244,579,358,228,40,245,580,359,229,41,243,581,233,360,38,240,578,231,361,36,241,576,232,362,37,242,577,670,669,672,671,134,72,484,478,176,132,73,485,479,174,133,74,483,477,175,71,137,487,481,179,69,135,488,482,177,70,136,486,480,178,129,78,490,476,182,130,79,491,474,180,131,80,489,475,181,77,128,493,472,185,75,126,494,473,183,76,127,492,471,184,680,677,679,678,192,151,59,501,145,193,152,57,502,146,194,150,58,503,144,154,195,55,504,148,155,196,56,505,149,153,197,54,506,147,190,157,50,499,143,191,158,48,500,141,189,156,49,498,142,160,186,53,495,139,161,187,51,496,140,159,188,52,497,138,689,690,691,692,217,325,20,331,563,218,326,18,332,561,216,324,19,330,562,328,220,23,334,566,329,221,21,335,564,327,219,22,333,565,215,323,15,337,558,213,321,16,338,559,214,322,17,336,560,319,211,14,340,557,320,212,12,341,555,318,210,13,339,556,697,698,700,699,589,621,647,633,605,590,622,645,634,603,588,623,646,635,604,620,592,643,632,601,618,593,644,630,602,619,591,642,631,600,595,612,638,624,611,596,613,636,625,609,594,614,637,626,610,615,598,641,627,607,616,599,639,628,608,617,597,640,629,606,661,662,664,663,281,263,413,406,428,279,261,411,407,426,280,262,412,405,427,259,277,416,409,424,260,278,414,410,425,258,276,415,408,423,272,269,419,404,434,270,267,417,402,432,271,268,418,403,433,265,275,422,400,430,266,273,420,401,431,264,274,421,399,429,682,681,684,683,31,86,347,572,65,32,84,345,570,63,30,85,346,571,64,89,34,343,575,68,87,35,344,573,66,88,33,342,574,67,29,652,654,655,653,27,658,656,659,657,28,648,649,650,651,83,25,349,569,62,81,26,350,567,60,82,24,348,568,61,693,694,696,695,201,519,545,531,507,202,520,543,532,508,203,521,544,533,509,522,200,548,534,510,523,198,546,535,511,524,199,547,536,512,207,525,551,537,513,208,526,549,538,514,209,527,550,539,515,528,206,554,540,516,529,204,552,541,517,530,205,553,542,518,666,665,668,667,446,96,304,288,309,444,97,305,289,310,445,98,303,290,311,99,442,300,291,308,100,443,301,292,306,101,441,302,293,307,437,94,295,286,315,435,95,296,287,316,436,93,294,285,317,90,440,298,282,314,91,438,299,283,312,92,439,297,284,313,674,673,676,675 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#299bf89dcaadd64e33422b05a87b398de7449d556bda64ba0ca787ebaa3d1bcb, 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 15:57:36 · history