Equation 677 Database

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Magma 0714c860becf…

magma 0714c860becf
Size
705
Isomorphism class hash
0714c860becf92ea667566a4a8ffa6ae163f62385e6a7b628b2c75b5b6866d2c
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 19:44:50
Display reorder
660,450,498,348,522,271,451,499,523,349,272,452,500,524,350,270,501,453,525,351,274,502,454,526,352,275,503,455,527,353,273,496,520,354,448,269,497,521,355,449,267,495,519,356,447,268,516,492,357,444,265,517,493,358,445,266,494,518,359,446,264,686,678,680,683,474,390,252,187,378,475,391,188,253,379,476,392,186,254,380,393,477,190,255,381,394,478,191,256,382,395,479,189,257,383,388,185,258,472,376,389,183,259,473,377,387,184,260,471,375,181,384,261,468,372,182,385,262,469,373,386,180,263,470,374,664,666,672,662,27,546,45,194,75,28,547,192,46,76,29,548,193,47,77,549,26,197,44,74,550,24,195,42,72,551,25,196,43,73,544,200,36,33,81,545,198,37,34,82,543,199,38,35,83,203,540,39,32,80,201,541,40,30,78,542,202,41,31,79,677,685,682,687,613,615,158,614,612,621,623,622,156,620,628,631,630,157,629,639,637,638,161,636,647,645,646,159,644,655,652,654,160,653,599,596,164,598,597,607,604,162,606,605,591,588,163,590,589,565,564,167,569,568,575,574,165,573,572,582,583,166,581,580,703,702,701,704,286,289,210,303,366,287,290,304,211,367,285,288,305,212,368,292,282,302,213,369,293,283,300,214,370,291,284,301,215,371,295,309,208,277,364,296,310,209,278,365,294,311,207,276,363,308,298,204,280,360,306,299,205,281,361,297,307,206,279,362,693,692,690,694,510,534,1,462,486,511,535,463,0,487,512,536,464,2,488,537,513,465,3,489,538,514,466,4,490,539,515,467,5,491,532,460,6,508,484,533,461,7,509,485,531,459,8,507,483,456,528,9,504,480,457,529,10,505,481,530,458,11,506,482,665,669,667,671,49,402,101,325,239,50,403,326,99,237,48,404,324,100,238,405,52,328,97,235,406,53,329,98,236,407,51,327,96,234,400,331,107,55,230,401,332,105,56,228,399,330,106,54,229,334,396,103,58,233,335,397,104,59,231,398,333,102,57,232,689,695,696,691,558,426,345,60,18,559,427,61,346,19,560,428,62,347,20,429,561,63,344,21,430,562,64,342,22,431,563,65,343,23,424,66,336,556,16,425,67,337,557,17,423,68,338,555,15,69,420,339,552,12,70,421,340,553,13,422,71,341,554,14,679,688,674,675,619,618,149,617,616,627,626,625,147,624,635,634,633,148,632,642,643,641,145,640,650,651,649,146,648,658,659,657,144,656,602,601,155,603,600,610,609,153,611,608,594,593,154,595,592,570,571,151,567,566,577,578,152,579,576,586,585,150,587,584,699,700,698,697,177,92,245,115,438,178,90,116,243,439,179,91,114,244,440,95,176,118,241,441,93,174,119,242,442,94,175,117,240,443,87,113,251,168,436,88,111,249,169,437,89,112,250,170,435,109,86,247,171,432,110,84,248,172,433,85,108,246,173,434,670,661,663,668,135,414,216,122,319,136,415,120,217,320,137,416,121,218,318,417,134,125,219,322,418,132,123,220,323,419,133,124,221,321,412,128,222,141,317,413,126,223,142,315,411,127,224,143,316,131,408,225,140,313,129,409,226,138,314,410,130,227,139,312,676,681,684,673 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#a6f8f14c2d1a7a50e2f04288a5c27cfc248015f3a737479d1ca25990a259c6e6, 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 19:44:50 · history