Equation 677 Database

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Magma 74aaae27f060…

magma 74aaae27f060
Size
705
Isomorphism class hash
74aaae27f0604dfb091c21fba446c75aaab1f3c86273cde4e5cad6c89ac684a9
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 20:39:36
Display reorder
660,605,8,611,606,618,6,625,631,626,638,645,7,646,651,658,11,585,591,586,598,9,545,551,546,558,10,565,571,566,578,425,3,431,426,438,445,4,451,446,456,465,5,471,466,478,2,485,491,486,498,1,505,511,506,518,0,525,531,526,538,704,692,687,693,603,257,608,604,612,255,623,628,624,632,643,256,644,648,652,253,583,588,584,592,254,543,548,544,552,252,563,568,564,572,423,263,428,424,432,443,261,448,444,452,463,262,468,464,472,259,483,488,484,492,260,503,508,504,512,258,523,528,524,532,691,688,698,700,333,143,297,34,154,141,334,298,35,155,335,142,33,299,153,139,332,296,30,150,140,330,294,31,151,138,331,295,32,152,324,134,288,25,145,325,132,289,26,146,326,133,290,24,144,137,327,291,28,148,135,328,292,29,149,136,329,293,27,147,669,664,672,667,45,233,217,405,83,231,46,218,406,81,47,232,407,216,82,229,44,220,404,79,230,42,221,402,80,228,43,219,403,78,36,239,223,396,74,37,237,224,397,72,38,238,222,398,73,235,39,226,399,77,236,40,227,400,75,234,41,225,401,76,675,665,678,680,614,18,615,613,602,19,634,635,633,622,654,20,653,655,642,21,594,595,593,582,22,554,555,553,542,23,574,575,573,562,434,16,435,433,422,453,17,459,458,457,474,15,475,473,462,12,494,495,493,482,13,514,515,513,502,14,534,535,533,522,689,686,703,696,619,196,601,600,617,197,639,620,621,637,659,195,641,640,657,192,599,581,580,597,193,559,540,541,557,194,579,561,560,577,439,202,420,421,437,440,203,442,441,455,479,201,461,460,477,198,499,481,480,497,199,519,501,500,517,200,539,520,521,537,695,702,699,701,607,215,616,610,609,213,627,636,630,629,647,214,650,656,649,211,587,596,590,589,212,547,556,550,549,210,567,576,570,569,427,206,436,430,429,447,204,454,450,449,467,205,476,470,469,209,487,496,490,489,207,507,516,510,509,208,527,536,530,529,694,697,685,690,417,246,68,273,52,247,418,66,274,53,419,248,275,67,51,249,416,71,272,48,250,414,69,270,49,251,415,70,271,50,408,244,63,264,58,409,245,64,265,59,410,243,65,266,57,240,411,62,267,54,241,412,60,268,55,242,413,61,269,56,684,681,662,661,369,182,309,91,393,180,370,310,92,394,371,181,90,311,395,185,368,308,94,392,183,366,306,95,390,184,367,307,93,391,360,188,300,89,384,361,186,301,87,385,362,187,302,88,386,191,363,303,85,387,189,364,304,86,388,190,365,305,84,389,674,666,679,683,321,158,285,114,357,156,322,286,115,358,323,157,116,287,359,161,320,284,117,356,159,318,282,118,354,160,319,283,119,355,312,164,276,112,348,313,162,277,113,349,314,163,278,111,350,167,315,279,108,351,165,316,280,109,352,166,317,281,110,353,668,663,673,676,381,123,176,345,96,124,382,174,346,97,383,125,347,175,98,122,380,179,344,99,120,378,177,342,100,121,379,178,343,101,372,129,171,336,102,373,130,172,337,103,374,131,173,338,104,128,375,170,339,105,126,376,168,340,106,127,377,169,341,107,677,671,682,670 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#c93f531644bb5fd38eabd6a6f62492ff6d9a38e5937df79a955f96fa67b29b12, 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 20:39:37 · history