Equation 677 Database

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Magma 5d8893b4281e…

magma 5d8893b4281e
Size
705
Isomorphism class hash
5d8893b4281e41808fc3f445ae14936eaa4716a86a4abb9ce83ffb79c3348c0f
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 16:56:33
Display reorder
660,84,515,500,501,513,85,535,520,521,533,86,495,480,481,493,87,435,420,421,433,88,453,448,449,452,89,475,460,461,473,90,635,620,621,633,91,655,640,641,653,92,615,600,601,613,555,93,541,540,553,575,94,561,560,573,595,95,581,580,593,685,699,695,686,249,511,512,514,508,250,531,532,534,528,251,491,492,494,488,248,431,432,434,428,246,457,458,459,446,247,471,472,474,468,240,631,632,634,628,241,651,652,654,648,242,611,612,614,608,551,243,552,554,548,571,244,572,574,568,591,245,592,594,588,690,693,687,694,71,304,352,388,218,69,305,353,389,216,70,303,351,387,217,67,300,348,384,221,68,301,349,385,219,66,302,350,386,220,62,310,358,394,224,60,311,359,395,222,61,309,357,393,223,306,65,354,390,227,307,63,355,391,225,308,64,356,392,226,665,670,662,676,110,181,164,7,168,108,182,162,8,169,109,180,163,6,170,113,184,167,10,171,111,185,165,11,172,112,183,166,9,173,116,187,159,5,174,114,188,160,3,175,115,186,161,4,176,190,119,158,0,177,191,117,156,2,178,189,118,157,1,179,663,680,674,671,13,505,507,506,516,14,525,527,526,536,12,485,487,486,496,16,425,427,426,436,17,443,445,444,447,15,465,467,466,476,19,625,627,626,636,20,645,647,646,656,18,605,607,606,616,545,22,547,546,556,565,23,567,566,576,585,21,587,586,596,700,702,698,703,78,517,518,519,509,79,537,538,539,529,80,497,498,499,489,81,437,438,439,429,82,440,441,442,450,83,478,477,479,469,76,638,637,639,629,77,657,658,659,649,75,618,617,619,609,557,72,558,559,549,577,73,578,579,569,598,74,597,599,589,696,689,688,701,96,504,502,503,510,97,524,522,523,530,98,484,482,483,490,99,424,422,423,430,100,456,454,455,451,101,464,462,463,470,102,624,622,623,630,103,644,642,643,650,104,604,602,603,610,544,105,542,543,550,564,106,562,563,570,584,107,582,583,590,692,704,691,697,155,202,340,207,234,153,203,341,208,235,154,201,339,209,236,151,198,336,206,237,152,199,337,204,238,150,200,338,205,239,146,193,346,213,232,144,194,347,214,233,145,192,345,215,231,196,149,342,212,228,197,147,343,210,229,195,148,344,211,230,681,669,666,677,27,412,316,364,128,28,413,317,365,126,29,411,315,363,127,26,408,312,360,131,24,409,313,361,129,25,410,314,362,130,33,418,322,370,123,34,419,323,371,124,35,417,321,369,125,414,32,318,366,122,415,30,319,367,120,416,31,320,368,121,679,667,684,672,260,283,57,292,376,258,284,58,293,377,259,282,59,291,375,263,286,56,288,372,261,287,54,289,373,262,285,55,290,374,255,281,48,298,382,256,279,49,299,383,257,280,50,297,381,277,254,51,294,378,278,252,52,295,379,276,253,53,296,380,683,682,673,661,40,400,142,265,328,41,401,143,266,329,39,399,141,264,327,36,396,138,268,324,37,397,139,269,325,38,398,140,267,326,46,406,133,271,334,47,407,134,272,335,45,405,132,270,333,402,42,136,274,330,403,43,137,275,331,404,44,135,273,332,678,675,668,664 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#49acd73e7fb20809c4c5aee6104079a0019ec0e0539c0b91c35b8b4466bd197d, 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 16:56:34 · history