Equation 677 Database

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Magma e1d201a8818d…

magma e1d201a8818d
Size
705
Isomorphism class hash
e1d201a8818d834fbce2f255916be723e117354b7f910ebee2e8aaddd9dc871a
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 21:14:01
Display reorder
704,118,131,66,154,116,132,67,152,117,133,68,153,114,134,69,150,115,135,70,151,113,136,71,149,64,109,137,145,65,107,138,143,63,108,139,144,112,60,140,148,110,61,141,146,111,62,142,147,126,127,125,129,130,128,124,122,119,120,121,123,700,703,701,702,658,659,656,657,650,651,648,649,654,655,652,653,642,643,640,641,646,647,645,644,638,639,636,637,620,622,623,621,612,614,615,613,616,618,619,617,634,632,635,633,626,624,627,625,630,628,631,629,84,85,86,87,88,611,90,91,92,93,94,89,691,690,689,688,361,393,329,353,359,394,330,354,360,392,331,355,364,389,332,356,362,390,333,357,363,391,334,358,327,367,384,351,328,365,385,352,326,366,383,350,370,323,387,347,368,324,388,348,369,325,386,349,373,371,372,376,374,375,379,377,381,382,380,378,675,674,672,673,233,261,211,267,234,262,209,268,235,260,210,266,236,257,214,263,237,258,212,264,238,259,213,265,206,231,252,273,207,232,253,274,208,230,251,272,227,205,255,269,228,203,256,270,229,204,254,271,241,239,240,244,242,243,247,245,249,250,248,246,681,680,683,682,435,408,59,429,436,409,57,430,434,407,58,428,431,411,55,425,432,412,56,426,433,410,54,427,50,441,414,420,48,442,415,421,49,440,413,419,437,53,417,423,438,51,418,424,439,52,416,422,443,444,445,446,447,448,449,450,454,452,453,451,693,694,692,695,169,200,222,159,167,201,223,160,168,202,221,158,172,199,225,155,170,197,226,156,171,198,224,157,220,175,191,165,218,173,192,166,219,174,193,164,178,216,194,161,176,217,195,162,177,215,196,163,181,179,180,184,182,183,187,185,189,190,188,186,698,699,697,696,554,532,99,544,555,530,100,542,556,531,98,543,553,528,95,540,551,529,96,541,552,527,97,539,105,560,538,550,106,561,536,548,104,562,537,549,559,101,534,546,557,102,535,547,558,103,533,545,518,519,520,517,515,516,524,525,522,523,521,526,686,687,684,685,33,7,403,20,34,8,401,18,35,6,402,19,32,10,406,23,30,11,404,21,31,9,405,22,398,24,5,15,399,25,3,16,400,26,4,17,27,397,0,14,28,395,2,12,29,396,1,13,43,44,42,46,47,45,41,39,36,37,38,40,661,660,663,662,317,287,339,310,318,288,340,308,319,289,338,309,320,290,335,306,321,291,336,307,322,292,337,305,345,315,293,301,346,316,294,299,344,314,295,300,311,341,296,304,312,342,297,302,313,343,298,303,280,278,279,276,277,275,286,284,281,282,283,285,676,677,678,679,479,460,83,471,480,458,81,472,481,459,82,470,482,456,79,467,483,457,80,468,484,455,78,469,74,485,466,477,72,486,464,478,73,487,465,476,488,77,462,473,489,75,463,474,490,76,461,475,502,500,501,498,499,497,493,491,495,496,494,492,665,664,667,666,572,597,503,603,573,598,504,604,574,596,505,602,571,593,506,599,569,594,507,600,570,595,508,601,509,563,588,609,510,564,589,610,511,565,587,608,566,512,591,605,567,513,592,606,568,514,590,607,581,582,583,584,585,586,579,580,577,575,576,578,670,669,671,668 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#e051b0f30a8ed34180a71689094d032915fc358f2733da2908c1415c24d3cdbe, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:14:02 · history