Equation 677 Database

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Magma 45390823081d…

magma 45390823081d
Size
705
Isomorphism class hash
45390823081dfd2169e5246c3be883864a3cfbd726b3867cb750b0f3f45f59c3
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 16:21:48
Display reorder
704,26,47,55,74,24,72,45,56,25,73,46,54,77,29,43,58,75,27,44,59,76,28,42,57,53,38,32,80,51,36,30,78,52,37,31,79,41,49,35,83,39,50,33,81,40,48,34,82,67,68,66,70,71,69,65,63,60,61,62,64,703,702,700,701,658,656,657,659,650,651,648,649,654,655,652,653,643,642,640,641,647,646,645,644,639,638,636,637,621,620,622,623,613,612,614,615,617,616,618,619,632,633,634,635,624,625,626,627,628,629,630,631,124,125,126,123,121,122,128,129,120,611,127,130,690,688,691,689,8,400,407,438,6,439,398,408,7,437,399,409,441,11,396,410,442,9,397,411,440,10,395,412,413,406,3,436,414,404,4,434,415,405,5,435,402,416,2,432,403,417,1,433,401,418,0,431,427,425,426,430,428,429,422,423,420,421,419,424,674,673,675,672,249,320,328,305,250,306,321,326,248,307,322,327,308,245,319,324,309,246,317,325,310,247,318,323,334,311,240,303,332,312,241,304,333,313,239,302,314,330,243,299,315,331,244,300,316,329,242,301,345,346,344,341,342,343,336,337,338,339,340,335,680,682,681,683,115,176,183,161,116,162,177,184,114,163,178,182,164,118,175,179,165,119,173,180,166,117,174,181,189,167,113,159,190,168,111,160,188,169,112,158,170,185,109,155,171,186,110,156,172,187,108,157,148,146,147,144,145,143,154,152,149,150,151,153,694,695,693,692,90,286,294,269,91,270,284,295,92,271,285,293,272,93,282,297,273,94,283,298,274,95,281,296,292,277,88,267,290,275,89,268,291,276,87,266,280,288,84,263,278,289,85,264,279,287,86,265,256,254,255,252,253,251,262,260,257,258,259,261,699,696,698,697,18,580,587,570,19,571,578,588,20,569,579,589,573,21,576,590,574,22,577,591,572,23,575,592,593,586,16,568,594,584,17,566,595,585,15,567,582,596,12,564,583,597,13,565,581,598,14,563,561,562,560,557,558,559,552,553,554,555,556,551,687,685,686,684,133,204,223,196,131,194,205,221,132,195,203,222,192,136,207,226,193,134,208,224,191,135,206,225,218,210,139,202,219,211,137,200,220,209,138,201,213,217,142,198,214,215,140,199,212,216,141,197,232,230,231,228,229,227,238,236,233,234,235,237,660,662,661,663,101,373,393,363,99,364,371,394,100,362,372,392,359,97,376,389,360,98,374,390,361,96,375,391,384,379,107,369,385,377,105,370,383,378,106,368,382,387,103,365,380,388,104,366,381,386,102,367,356,357,358,355,353,354,347,348,352,350,351,349,677,679,676,678,498,461,477,446,499,447,462,478,497,448,463,476,445,501,464,473,443,502,465,474,444,500,466,475,468,459,496,452,469,460,494,453,467,458,495,454,455,471,492,451,456,472,493,449,457,470,491,450,490,488,489,486,487,485,481,479,483,484,482,480,664,666,665,667,603,526,535,511,604,509,524,533,602,510,525,534,514,599,522,538,512,600,523,536,513,601,521,537,530,517,609,506,531,515,610,507,532,516,608,508,520,529,605,505,518,527,606,503,519,528,607,504,543,544,542,539,540,541,549,550,547,545,546,548,669,668,670,671 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#2e8e4ac0a437874a6303a2bb1c968f3f1df955f15fe5de36e1349d884d5d267c, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 16:21:51 · history