Equation 677 Database

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Magma 7e98aedf6ee3…

magma 7e98aedf6ee3
Size
705
Isomorphism class hash
7e98aedf6ee38f103a177458e5bbcdf3f186144e910954c90a6deb22659cc0d1
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 16:22:44
Display reorder
660,10,513,505,507,508,11,528,533,525,527,9,488,493,485,487,433,6,428,425,427,453,7,451,448,450,8,473,468,465,467,0,633,628,625,627,2,653,648,645,647,1,613,608,605,607,553,4,548,545,547,565,573,5,568,567,593,3,588,585,587,688,699,690,694,33,506,511,514,503,34,523,526,531,534,35,483,486,491,494,426,32,423,431,434,456,30,455,457,446,31,466,463,471,474,24,626,623,631,634,25,646,643,651,654,26,606,603,611,614,546,27,543,551,554,571,566,28,563,574,586,29,583,591,594,695,686,692,687,128,364,88,316,400,126,401,365,89,317,127,399,363,87,315,360,131,396,84,312,361,129,397,85,313,130,362,398,86,314,123,370,406,94,322,124,371,407,95,323,125,369,405,93,321,366,122,402,90,318,91,367,120,403,319,368,121,404,92,320,664,661,678,668,205,388,179,183,151,206,152,389,177,184,204,150,387,178,185,384,208,154,175,182,385,209,155,176,180,207,386,153,174,181,211,394,149,170,189,212,395,147,168,190,210,393,148,169,191,390,214,145,173,188,171,391,215,146,186,392,213,144,172,187,673,672,662,675,21,509,504,502,516,22,536,529,524,522,23,496,489,484,482,429,20,436,424,422,445,18,447,444,443,19,469,476,464,462,12,629,636,624,622,13,649,656,644,642,14,609,616,604,602,549,15,556,544,542,564,569,16,576,562,589,17,596,584,582,700,702,698,703,61,518,519,510,517,62,538,537,539,530,60,497,498,499,490,438,64,437,439,430,440,65,441,442,452,63,478,477,479,470,67,637,638,639,630,68,657,658,659,650,66,617,618,619,610,557,70,558,559,550,579,578,71,577,570,597,69,598,599,590,691,701,685,697,219,515,500,501,512,220,532,535,521,520,221,492,495,480,481,435,218,432,421,420,459,216,458,454,449,217,475,472,461,460,225,635,632,620,621,226,655,652,641,640,227,615,612,600,601,555,224,552,540,541,561,575,222,572,560,595,223,592,581,580,689,704,693,696,143,103,328,118,80,141,78,104,329,119,142,79,102,327,117,106,139,83,324,114,107,140,81,325,115,138,105,82,326,116,134,101,75,334,109,132,99,76,335,110,133,100,77,333,108,97,137,74,330,112,331,98,135,72,113,96,136,73,332,111,680,665,670,679,158,376,58,352,200,156,198,377,59,353,157,199,375,57,351,372,161,203,54,348,373,159,201,55,349,160,374,202,56,350,164,382,195,49,358,162,383,196,50,359,163,381,197,48,357,378,167,194,52,354,53,379,165,192,355,380,166,193,51,356,667,681,684,674,42,261,275,280,307,43,308,262,273,281,44,306,263,274,279,260,45,310,271,276,258,46,311,272,277,47,259,309,270,278,40,252,305,266,286,41,253,303,264,287,39,254,304,265,285,255,36,301,269,282,267,256,37,302,283,257,38,300,268,284,683,677,676,671,288,340,228,241,412,289,413,341,229,242,290,411,339,230,240,336,291,408,231,244,337,292,409,232,245,293,338,410,233,243,294,346,418,234,247,295,347,419,235,248,296,345,417,236,246,342,297,414,237,250,238,343,298,415,251,344,299,416,239,249,669,663,682,666 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#2ec821928dae411f986b7c636eee0f3d0451d16a0e775a52641e8351195889f9, 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 16:22:44 · history