Equation 677 Database

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Magma 81a62a77df0f…

magma 81a62a77df0f
Size
705
Isomorphism class hash
81a62a77df0fcd35944922f12d9316a6ea5eae9aedfe2f560699a4e1d392b1d8
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 17:20:15
Display reorder
660,570,615,251,603,583,568,613,249,601,584,569,614,250,602,585,611,573,254,599,582,252,571,612,600,580,610,572,253,598,581,576,606,257,594,589,574,604,255,592,590,575,605,256,593,591,609,579,260,597,588,607,577,258,595,586,608,578,259,596,587,687,688,686,685,443,436,202,169,329,441,437,200,167,327,442,435,201,168,328,439,446,205,165,332,203,444,440,166,330,438,445,204,164,331,449,434,197,160,324,447,432,198,158,325,448,433,199,159,326,430,452,196,163,323,431,450,194,161,321,429,451,195,162,322,703,704,701,702,47,92,559,244,50,48,93,560,245,51,49,94,561,243,52,95,46,558,247,53,556,44,96,248,54,97,45,557,246,55,38,90,565,242,56,39,91,566,240,57,40,89,567,241,58,86,41,564,238,59,87,42,562,239,60,88,43,563,237,61,671,672,670,669,172,210,461,355,341,170,211,459,356,339,171,209,460,354,340,206,175,464,351,344,462,173,207,352,342,208,174,463,353,343,178,216,456,346,336,176,217,457,347,337,177,215,458,345,338,212,181,455,349,335,213,179,453,350,333,214,180,454,348,334,679,680,678,677,368,482,62,471,186,366,480,63,472,187,367,481,64,473,185,478,364,65,474,182,66,365,479,475,183,477,363,67,476,184,359,488,68,469,192,357,486,69,470,193,358,487,70,468,191,484,362,71,465,188,485,360,72,466,189,483,361,73,467,190,692,691,690,689,518,501,396,540,527,516,502,397,541,525,517,503,398,542,526,504,514,395,539,530,393,515,505,537,528,506,513,394,538,529,524,507,402,546,533,522,508,403,547,531,523,509,404,548,532,510,520,401,545,536,511,521,399,543,534,512,519,400,544,535,699,700,698,697,125,110,148,103,143,126,111,146,101,144,127,112,147,102,145,113,124,151,99,142,149,122,114,100,140,115,123,150,98,141,131,116,154,109,134,132,117,152,107,135,133,118,153,108,136,119,130,157,105,137,120,128,155,106,138,121,129,156,104,139,663,664,662,661,630,623,222,267,410,628,624,223,268,408,629,622,221,269,409,626,633,218,270,406,219,631,627,271,407,625,632,220,272,405,636,621,228,265,416,634,619,229,266,414,635,620,227,264,415,617,639,224,261,412,618,637,225,262,413,616,638,226,263,411,682,683,684,681,654,652,20,655,653,658,656,18,659,657,650,649,19,651,648,31,236,23,549,24,21,640,641,642,643,645,646,22,647,644,235,35,15,552,27,233,36,16,550,25,234,37,17,551,26,34,231,14,555,30,32,232,12,553,28,33,230,13,554,29,695,696,693,694,391,377,490,1,75,392,375,491,0,76,390,376,489,2,74,380,387,493,3,78,494,388,378,4,79,379,389,492,5,77,382,372,496,6,81,383,373,497,7,82,381,374,495,8,80,371,385,499,9,84,369,386,500,10,85,370,384,498,11,83,667,668,665,666,312,299,428,294,281,313,297,426,295,279,314,298,427,296,280,302,311,424,293,284,425,309,300,291,282,301,310,423,292,283,318,305,419,285,276,319,303,417,286,277,320,304,418,287,278,308,317,422,288,275,306,315,420,289,273,307,316,421,290,274,675,676,673,674 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#4f47b623d963c151ceba4da4fdb4170837133dc09cb743e53f258ef94ac4defc, 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 17:20:16 · history