Equation 677 Database

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Magma 165612efaebe…

magma 165612efaebe
Size
705
Isomorphism class hash
165612efaebed382ed57266a94e39f29848c6b88fd313a28034e070c1f7e27ac
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 18:18:42
Display reorder
660,534,12,392,334,345,13,343,532,390,335,11,344,533,391,336,537,348,8,395,333,535,346,9,393,331,536,347,10,394,332,351,3,398,540,340,349,4,396,538,341,350,2,397,539,342,354,6,401,543,339,541,352,7,399,337,353,5,400,542,338,675,683,674,676,62,212,313,364,104,213,105,63,314,365,214,106,64,315,366,65,107,215,316,363,66,108,216,317,361,67,109,217,318,362,102,218,311,68,355,103,219,312,69,356,101,220,310,70,357,98,221,307,71,358,72,99,222,308,359,100,223,309,73,360,672,663,670,666,510,322,232,428,462,323,460,508,230,426,324,461,509,231,427,513,465,321,235,431,511,463,319,233,429,512,464,320,234,430,468,328,227,516,434,466,329,228,514,432,467,330,229,515,433,471,327,226,519,437,517,469,325,224,435,470,326,225,518,436,680,682,679,685,440,18,253,180,174,19,172,438,254,178,17,173,439,255,179,443,177,14,256,183,441,175,15,257,181,442,176,16,258,182,169,24,251,446,186,170,25,252,444,184,171,23,250,445,185,653,20,654,657,656,447,1,21,248,187,0,22,249,448,188,703,700,704,698,558,272,474,522,582,273,580,556,472,520,271,581,557,473,521,561,585,275,477,525,559,583,276,475,523,560,584,274,476,524,588,278,480,564,528,586,279,478,562,526,587,277,479,563,527,591,281,483,567,531,565,589,282,481,529,590,280,482,566,530,693,692,691,690,594,48,498,247,570,49,568,592,496,245,47,569,593,497,246,597,573,44,501,243,595,571,45,499,244,596,572,46,500,242,576,39,504,600,238,574,40,502,598,236,575,38,503,599,237,579,42,507,603,241,601,577,43,505,239,578,41,506,602,240,667,668,665,664,122,84,196,143,150,85,151,123,197,144,83,149,124,195,145,125,146,80,199,142,126,147,81,200,140,127,148,82,198,141,156,75,194,128,134,157,76,192,129,135,155,74,193,130,136,152,78,190,131,137,132,153,79,191,138,154,77,189,133,139,695,694,696,689,642,120,404,93,606,121,604,640,402,94,119,605,641,403,92,645,609,116,407,96,643,607,117,405,97,644,608,118,406,95,612,111,410,648,91,610,112,408,646,89,611,110,409,647,90,615,114,413,651,87,649,613,115,411,88,614,113,412,650,86,686,688,673,677,160,51,451,381,208,52,206,158,449,379,50,207,159,450,380,163,211,54,454,384,161,209,55,452,382,162,210,53,453,383,203,57,457,166,387,204,58,455,164,385,205,56,456,165,386,658,60,659,652,655,167,202,61,458,388,201,59,459,168,389,699,702,697,701,369,299,630,259,33,300,34,367,628,260,298,32,368,629,261,372,36,295,633,262,370,37,296,631,263,371,35,297,632,264,31,305,636,375,265,29,306,634,373,266,30,304,635,374,267,27,301,639,378,268,376,28,302,637,269,26,303,638,377,270,661,662,669,671,546,284,416,486,618,285,616,544,414,484,283,617,545,415,485,549,621,287,419,489,547,619,288,417,487,548,620,286,418,488,624,290,422,552,492,622,291,420,550,490,623,289,421,551,491,627,293,425,555,495,553,625,294,423,493,626,292,424,554,494,687,684,681,678 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#789271f8e1620c5f8875a1b32dfd6da1b71c443ca3fc9082ace33bb0fcd8a22c, 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 18:18:43 · history