Equation 677 Database

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Magma 7b4735780fc4…

magma 7b4735780fc4
Size
705
Isomorphism class hash
7b4735780fc4f216191ea83ed7ddd7885052aa207f409cd0d45e829323987086
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 20:43:42
Display reorder
660,62,162,575,475,415,63,576,476,416,160,61,161,577,477,417,574,58,165,474,414,59,572,163,472,412,60,573,164,473,413,53,581,168,481,421,482,54,582,166,422,52,583,167,483,423,580,56,171,480,420,578,57,169,478,418,579,55,170,479,419,676,678,685,684,100,399,403,360,384,101,404,358,382,397,102,398,405,359,383,402,103,395,363,387,104,400,396,361,385,105,401,394,362,386,106,409,390,355,379,356,107,410,388,380,108,411,389,357,381,408,109,393,354,378,406,110,391,352,376,407,111,392,353,377,662,669,661,663,95,427,252,367,511,96,250,368,512,428,94,429,251,369,513,255,98,426,366,510,99,253,424,364,508,97,254,425,365,509,93,247,433,373,517,374,91,248,434,518,92,249,435,375,519,246,89,432,372,516,244,90,430,370,514,245,88,431,371,515,679,675,677,673,202,22,3,523,119,203,4,524,117,20,204,21,5,525,118,2,205,25,522,115,206,1,23,520,116,207,0,24,521,114,200,636,637,641,638,649,201,645,644,646,199,653,652,657,654,629,196,628,633,632,6,197,26,526,113,7,198,27,527,112,703,697,704,698,71,43,587,487,223,72,588,488,224,44,70,45,589,489,225,586,74,42,486,222,75,584,40,484,220,73,585,41,485,221,69,593,49,493,229,494,67,594,50,230,68,595,51,495,231,592,65,48,492,228,590,66,46,490,226,591,64,47,491,227,693,691,690,694,262,194,499,451,178,263,500,452,179,195,264,193,501,453,180,498,265,190,450,181,266,496,191,448,182,267,497,192,449,183,260,505,185,457,176,458,261,506,186,177,259,507,184,459,175,504,256,188,456,172,502,257,189,454,173,503,258,187,455,174,670,665,672,668,16,292,314,317,290,14,315,318,291,293,15,294,313,316,289,310,19,295,320,286,17,311,296,321,287,18,312,297,319,288,11,305,298,323,281,324,12,306,299,282,13,304,300,322,280,308,10,301,326,284,309,8,302,327,285,307,9,303,325,283,695,689,696,692,156,335,343,619,543,154,344,620,544,336,155,334,345,621,545,342,159,338,618,542,157,340,339,616,540,158,341,337,617,541,151,349,333,625,549,626,152,350,331,550,153,351,332,627,551,348,150,329,624,548,346,148,330,622,546,347,149,328,623,547,681,688,683,674,137,611,126,555,129,138,127,556,130,612,136,613,125,557,128,122,140,610,554,132,141,123,608,552,133,139,124,609,553,131,143,639,643,642,640,650,144,647,651,648,142,655,659,658,656,634,146,635,631,630,121,147,614,558,135,120,145,615,559,134,701,699,702,700,77,439,563,463,216,78,564,464,214,440,76,441,565,465,215,562,80,438,462,219,81,560,436,460,217,79,561,437,461,218,83,569,445,469,211,470,84,570,446,212,82,571,447,471,213,568,86,444,468,210,566,87,442,466,208,567,85,443,467,209,667,666,664,671,268,239,531,34,599,269,532,35,600,240,270,238,533,36,601,530,271,242,37,598,272,528,243,38,596,273,529,241,39,597,274,537,237,32,605,33,275,538,235,606,276,539,236,31,607,536,277,233,28,604,534,278,234,29,602,535,279,232,30,603,686,687,682,680 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#cd941b7de786c28317b7a103413c14ee77b5f1d3c398e3760811607e92439ad2, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 20:43:43 · history