Equation 677 Database

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Magma f72223e72b8f…

magma f72223e72b8f
Size
705
Isomorphism class hash
f72223e72b8f95f4a7acf6ece7f1bb8e7de5316517408f48e195973a40c00ad2
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 16:56:50
Display reorder
660,265,333,358,353,329,266,334,359,351,327,264,335,357,352,328,268,332,354,349,325,269,330,355,350,326,267,331,356,348,324,263,339,364,344,320,261,340,365,342,318,262,341,363,343,319,338,259,360,347,323,336,260,361,345,321,337,258,362,346,322,686,673,683,676,137,466,21,370,508,135,467,22,371,509,136,465,23,369,507,133,462,20,366,504,134,463,18,367,505,132,464,19,368,506,128,472,12,376,514,126,473,13,377,515,127,471,14,375,513,468,131,15,372,510,469,129,16,373,511,470,130,17,374,512,665,664,667,662,41,496,148,454,526,39,497,149,455,527,40,495,147,453,525,37,492,144,450,522,38,493,145,451,523,36,494,146,452,524,32,502,139,460,532,30,503,140,461,533,31,501,138,459,531,498,35,142,456,528,499,33,143,457,529,500,34,141,458,530,679,674,680,677,102,518,176,29,182,103,516,174,27,180,104,517,175,28,181,105,521,179,25,185,106,519,177,26,183,107,520,178,24,184,108,647,648,644,645,109,655,656,653,652,110,639,640,636,637,612,111,613,617,616,623,112,624,621,620,631,113,632,629,628,704,699,703,698,270,382,238,442,538,271,383,239,443,539,272,381,237,441,537,273,378,234,438,534,274,379,235,439,535,275,380,236,440,536,276,388,244,448,544,277,389,245,449,545,278,387,243,447,543,384,279,240,444,540,385,280,241,445,541,386,281,242,446,542,690,689,693,692,91,158,550,162,478,92,156,551,163,479,90,157,549,164,477,94,161,546,165,474,95,159,547,166,475,93,160,548,167,476,97,153,556,168,484,98,154,557,169,485,96,155,555,170,483,152,100,552,171,480,150,101,553,172,481,151,99,554,173,482,663,670,666,668,57,409,296,430,4,58,410,294,431,5,59,408,295,429,3,56,412,299,426,1,54,413,297,427,0,55,411,298,428,2,63,407,302,436,10,64,405,300,437,11,65,406,301,435,9,403,62,305,432,6,404,60,303,433,7,402,61,304,434,8,695,694,696,691,308,586,604,418,568,306,587,605,419,569,307,585,603,417,567,311,582,600,414,564,309,583,601,415,565,310,584,602,416,566,314,592,610,424,574,312,593,611,425,575,313,591,609,423,573,588,317,606,420,570,589,315,607,421,571,590,316,608,422,572,685,688,682,675,72,580,489,598,562,73,581,490,599,563,74,579,491,597,561,75,576,488,594,558,76,577,486,595,559,77,578,487,596,560,70,650,646,651,649,71,658,654,659,657,69,642,638,643,641,619,66,618,615,614,626,67,622,627,625,634,68,630,635,633,701,697,700,702,123,194,220,199,225,124,192,221,200,226,125,193,219,198,227,122,197,216,202,224,120,195,217,203,222,121,196,218,201,223,114,189,211,205,231,115,190,212,206,232,116,191,210,204,233,188,117,214,208,230,186,118,215,209,228,187,119,213,207,229,671,661,672,669,79,398,251,293,48,80,396,249,291,49,78,397,250,292,50,82,401,247,289,51,83,399,248,290,52,81,400,246,288,53,85,393,257,284,46,86,394,255,282,47,84,395,256,283,45,392,88,253,287,42,390,89,254,285,43,391,87,252,286,44,687,681,678,684 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#49acd73e7fb20809c4c5aee6104079a0019ec0e0539c0b91c35b8b4466bd197d, 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 16:56:51 · history