Equation 677 Database

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Magma da57eddbe15d…

magma da57eddbe15d
Size
705
Isomorphism class hash
da57eddbe15d2b6a4348882db4dc4c72bdd0da38261ab04884e9d3ff8fef67a1
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 19:11:31
Display reorder
660,382,240,93,582,464,94,380,580,241,462,381,239,92,581,463,89,385,585,236,467,383,90,583,237,465,91,384,584,238,466,388,99,588,246,470,386,100,586,247,468,387,98,587,245,469,95,391,591,242,473,96,389,589,243,471,97,390,590,244,472,677,686,680,673,71,394,128,343,594,129,72,341,392,592,73,393,130,342,593,127,74,339,397,597,75,125,340,395,595,126,76,338,396,596,69,134,334,400,600,70,135,332,398,598,68,136,333,399,599,133,65,337,403,603,131,66,335,401,601,132,67,336,402,602,665,668,671,662,346,370,11,558,606,9,344,556,368,604,345,369,10,557,605,7,349,561,373,609,347,8,559,371,607,6,348,560,372,608,352,17,564,376,612,350,15,562,374,610,351,16,563,375,611,13,355,567,379,615,14,353,565,377,613,12,354,566,378,614,674,684,688,676,4,499,326,406,46,327,5,404,497,47,3,498,328,405,48,329,1,409,502,45,0,330,407,500,43,331,2,408,501,44,174,324,412,505,52,175,325,410,503,50,173,323,411,504,51,320,653,654,657,656,321,171,413,506,49,322,172,414,507,42,698,697,704,703,618,259,192,510,570,193,616,508,257,568,617,258,191,509,569,188,621,513,255,573,619,189,511,256,571,190,620,512,254,572,624,198,516,250,576,622,199,514,248,574,623,197,515,249,575,194,627,519,253,579,195,625,517,251,577,196,626,518,252,578,694,691,693,689,21,428,31,300,310,32,22,301,426,308,23,427,30,299,309,34,20,296,431,313,18,35,297,429,311,33,19,298,430,312,27,37,306,434,316,28,38,307,432,314,29,36,305,433,315,40,26,302,437,319,41,24,303,435,317,39,25,304,436,318,669,672,670,663,632,282,106,633,219,104,629,628,283,220,631,281,105,630,218,102,638,639,278,222,634,103,635,279,223,101,636,637,280,221,645,112,644,273,217,641,110,640,274,215,643,111,642,272,216,108,651,650,276,213,109,647,646,277,214,107,649,648,275,212,695,696,692,690,235,358,292,546,440,290,233,544,356,438,234,357,291,545,439,295,231,549,361,443,232,293,547,359,441,294,230,548,360,442,226,287,552,364,446,224,288,550,362,444,225,289,551,363,445,286,229,555,367,449,284,227,553,365,447,285,228,554,366,448,685,683,678,675,488,162,148,140,417,149,486,141,160,415,487,161,150,142,416,151,491,139,165,420,489,152,137,163,418,153,490,138,164,419,494,154,146,168,423,492,155,147,166,421,493,156,145,167,422,157,659,658,652,655,158,495,143,169,424,159,496,144,170,425,701,700,699,702,55,476,121,178,534,119,53,176,474,532,54,475,120,177,533,124,58,181,479,537,56,122,179,477,535,123,57,180,478,536,61,116,184,482,540,59,117,182,480,538,60,118,183,481,539,115,64,187,485,543,113,62,185,483,541,114,63,186,484,542,661,664,667,666,208,522,267,81,452,268,206,82,520,450,207,521,266,80,451,270,211,77,525,455,209,271,78,523,453,269,210,79,524,454,203,265,87,528,458,204,263,88,526,456,205,264,86,527,457,261,202,83,531,461,262,200,84,529,459,260,201,85,530,460,687,681,679,682 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#8ecda3bf937b7c39d65eafcd0523fd56cf367f983a83102877b0cefff256addf, 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 19:11:31 · history