Equation 677 Database

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Magma eaebf1dbb0e0…

magma eaebf1dbb0e0
Size
705
Isomorphism class hash
eaebf1dbb0e0f513712dbb73f80b0d21f2ca06056fe0c22be67ab3d1e3bf7293
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 21:16:49
Display reorder
660,530,161,89,543,339,531,162,340,90,544,529,160,341,88,542,533,157,342,85,546,534,158,343,86,547,532,159,344,87,545,345,528,95,167,541,346,526,96,168,539,347,527,94,166,540,524,348,91,163,537,525,349,92,164,538,523,350,93,165,536,674,686,687,675,36,234,126,267,408,37,235,409,124,268,38,236,407,125,269,39,233,411,122,270,40,231,412,123,271,41,232,410,121,272,406,42,132,240,273,404,43,130,241,274,405,44,131,242,275,45,402,128,239,276,46,403,129,237,277,47,401,127,238,278,670,672,667,665,250,286,16,138,457,251,287,458,17,136,249,285,456,15,137,253,289,460,12,134,254,290,461,13,135,252,288,459,14,133,455,248,22,284,144,453,246,23,282,142,454,247,21,283,143,244,451,18,280,140,245,452,19,281,141,243,450,20,279,139,676,673,679,683,620,622,66,624,621,628,630,629,67,632,612,614,613,68,616,644,646,645,69,648,652,654,653,70,656,637,638,636,71,640,605,604,64,606,608,588,589,65,590,592,597,596,63,598,600,573,572,60,577,576,582,581,61,580,584,72,218,62,217,388,703,698,699,704,371,358,179,506,106,372,359,107,180,507,370,357,108,178,505,374,361,105,175,509,375,362,103,176,510,373,360,104,177,508,97,369,170,356,504,98,367,171,354,502,99,368,169,355,503,365,100,173,352,500,366,101,174,353,501,364,102,172,351,499,690,691,694,689,518,156,208,298,445,519,154,446,209,299,517,155,444,210,297,521,152,448,207,301,522,153,449,205,302,520,151,447,206,300,443,516,214,147,296,441,514,215,145,294,442,515,216,146,295,512,439,213,150,292,513,440,211,148,293,511,438,212,149,291,661,669,662,666,117,421,185,81,31,115,422,32,186,79,116,420,30,184,80,120,424,34,181,84,118,425,35,182,82,119,423,33,183,83,29,112,191,419,76,27,113,192,417,77,28,114,190,418,78,111,25,187,415,75,109,26,188,416,73,110,24,189,414,74,692,695,696,693,567,469,204,263,334,568,470,335,202,261,566,468,333,203,262,570,472,337,200,266,571,473,338,201,264,569,471,336,199,265,332,565,195,467,258,330,563,193,465,259,331,564,194,466,260,561,328,198,463,257,562,329,196,464,255,560,327,197,462,256,684,688,681,678,626,627,58,625,623,634,635,631,59,633,618,619,615,57,617,650,651,647,54,649,658,659,655,55,657,642,643,639,56,641,607,610,49,611,609,591,594,50,595,593,599,602,48,603,601,579,578,52,575,574,586,583,53,587,585,474,363,51,535,413,702,701,700,697,494,555,224,396,322,495,556,323,222,397,493,554,321,223,395,497,558,325,220,399,498,559,326,221,400,496,557,324,219,398,320,492,230,553,394,318,490,228,551,392,319,491,229,552,393,488,316,226,549,390,489,317,227,550,391,487,315,225,548,389,671,668,664,663,482,433,1,310,383,483,434,384,0,311,481,432,382,2,309,485,436,386,3,313,486,437,387,4,314,484,435,385,5,312,381,480,6,431,308,379,478,7,429,306,380,479,8,430,307,476,377,9,427,304,477,378,10,428,305,475,376,11,426,303,682,685,677,680 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#e2a478bba1a9cde7c476f091d01301457f542f6a1b857d9784efc8df77c998e9, 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 21:16:50 · history