Equation 677 Database

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Magma a5bf8e0cd730…

magma a5bf8e0cd730
Size
705
Isomorphism class hash
a5bf8e0cd7306da55ac900696cf3a9e1c25df67b2b0dcad13991cd087b5794e6
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 21:57:35
Display reorder
660,29,79,212,340,216,27,80,210,341,217,28,78,211,339,218,82,25,215,336,219,83,213,337,220,26,81,24,214,338,221,35,207,77,346,222,33,208,75,347,223,34,209,76,345,224,206,31,73,342,225,343,204,32,74,226,205,30,72,344,227,675,679,684,686,15,323,328,306,200,16,321,329,307,198,17,322,327,308,199,319,14,324,309,203,320,325,310,201,12,318,13,326,311,202,21,334,314,304,195,22,335,312,305,196,23,333,313,303,197,330,20,317,300,194,301,331,18,315,192,332,19,316,302,193,669,661,662,671,2,454,110,550,123,1,455,108,551,124,0,453,109,549,125,450,5,113,546,122,451,111,547,120,3,452,4,112,548,121,8,116,460,556,129,6,114,461,557,130,7,115,459,555,131,119,11,456,552,128,553,117,9,457,126,118,10,458,554,127,682,680,674,678,144,388,283,393,424,145,389,284,394,425,146,387,282,395,423,384,147,286,392,420,385,287,390,421,148,386,149,285,391,422,150,645,646,647,650,151,652,654,655,658,152,637,638,639,642,613,153,614,616,617,623,621,154,622,626,628,155,630,631,634,704,701,703,697,231,86,562,466,490,232,84,563,467,491,233,85,561,465,489,89,230,558,462,486,87,559,463,487,228,88,229,560,464,488,237,568,92,472,496,238,569,90,473,497,239,567,91,471,495,564,236,95,468,492,469,565,234,93,493,566,235,94,470,494,691,692,694,689,132,478,538,442,373,133,479,539,443,374,134,477,537,441,372,474,135,534,438,376,475,535,439,377,136,476,137,536,440,375,138,544,484,448,379,139,545,485,449,380,140,543,483,447,378,540,141,480,444,382,445,541,142,481,383,542,143,482,446,381,663,668,667,664,265,52,352,171,430,266,53,353,172,431,264,51,351,173,429,48,268,348,170,426,49,349,168,427,269,50,267,350,169,428,271,358,58,177,436,272,359,59,178,437,270,357,57,179,435,354,274,54,176,432,174,355,275,55,433,356,273,56,175,434,695,690,696,693,64,586,365,406,604,65,587,363,407,605,63,585,364,405,603,582,60,361,402,600,583,362,403,601,61,584,62,360,404,602,70,371,592,412,610,71,369,593,413,611,69,370,591,411,609,367,66,588,408,606,409,368,67,589,607,366,68,590,410,608,677,688,673,685,190,399,598,418,280,191,400,599,419,281,189,401,597,417,279,398,186,594,414,276,396,595,415,277,187,397,188,596,416,278,181,651,648,649,644,182,659,656,657,653,180,643,640,641,636,619,184,618,615,612,625,627,185,624,620,635,183,632,633,629,700,698,702,699,165,526,502,574,291,166,527,503,575,292,167,525,501,573,293,522,164,498,570,290,523,499,571,288,162,524,163,500,572,289,156,508,532,580,297,157,509,533,581,298,158,507,531,579,299,504,159,528,576,296,577,505,160,529,294,506,161,530,578,295,670,672,665,666,99,254,514,248,39,100,252,515,246,40,101,253,513,247,41,257,98,510,251,38,255,511,249,36,96,256,97,512,250,37,105,520,260,243,45,106,521,258,244,46,107,519,259,245,47,516,104,263,242,44,240,517,102,261,42,518,103,262,241,43,676,687,681,683 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#fdf5f382e471d95c048f9fa2e9b8340aa5eb614276b1c155a6fb7129b8435eb8, 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 21:57:36 · history