Equation 677 Database

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Magma 41a3fc68643d…

magma 41a3fc68643d
Size
705
Isomorphism class hash
41a3fc68643d515b44518f2c0c8845b2fe267ef58fc0a3b8194aa6590b7affb7
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 20:06:54
Display reorder
660,142,436,376,304,277,143,278,434,374,305,141,276,435,375,303,432,145,273,372,307,433,146,274,373,308,431,144,275,371,306,148,283,442,382,302,284,440,380,149,300,441,282,381,147,301,279,438,378,151,298,280,439,379,152,299,281,437,377,150,297,675,683,677,684,82,201,236,215,189,83,190,202,234,213,81,191,203,235,214,204,85,192,232,218,205,86,193,233,216,206,84,194,231,217,88,195,207,227,221,196,208,225,89,219,209,197,226,87,220,198,210,230,91,224,199,211,228,92,222,200,212,229,90,223,664,672,661,669,240,534,448,54,293,241,291,532,446,52,242,292,533,447,53,530,239,296,444,50,531,237,294,445,51,529,238,295,443,49,246,288,540,454,45,289,538,452,247,43,539,290,453,248,44,287,536,450,245,48,285,537,451,243,46,286,535,449,244,47,678,687,681,673,38,63,16,615,57,39,58,64,17,613,37,56,62,18,614,66,41,60,15,618,67,42,61,13,616,65,40,59,14,617,36,653,654,652,659,637,638,636,34,643,646,645,644,35,651,620,622,621,32,624,628,630,629,33,635,55,68,12,31,619,704,701,702,697,157,412,320,546,510,158,508,410,318,544,156,509,411,319,545,408,153,506,316,542,409,154,507,317,543,407,155,505,315,541,163,516,418,311,552,514,416,309,164,550,417,515,310,162,551,512,414,314,159,548,513,415,312,160,549,511,413,313,161,547,689,693,691,692,97,491,522,255,26,98,27,489,520,256,96,25,490,521,257,487,93,29,518,258,488,94,30,519,259,486,95,28,517,260,103,24,497,528,253,22,495,526,104,254,496,23,527,102,252,20,493,524,99,249,21,494,525,100,250,19,492,523,101,251,667,662,666,668,324,72,121,400,171,325,172,73,122,398,326,173,74,120,399,71,323,174,117,396,69,321,175,118,397,70,322,176,119,395,330,169,78,127,406,170,79,128,331,404,80,168,126,332,405,165,77,123,329,402,166,75,124,327,403,167,76,125,328,401,694,690,695,696,132,350,388,570,343,133,344,348,386,568,134,342,349,387,569,346,131,339,384,566,347,129,340,385,567,345,130,341,383,565,138,334,356,394,576,335,354,392,139,574,355,333,393,140,575,337,352,390,137,572,338,353,391,135,573,336,351,389,136,571,676,685,674,680,183,362,500,369,484,184,482,363,498,367,185,483,361,499,368,358,186,480,503,365,359,187,481,501,366,360,188,479,502,364,181,657,655,658,656,641,639,642,182,640,647,649,650,180,648,626,625,627,177,623,633,631,634,178,632,485,357,504,179,370,699,698,703,700,1,594,424,460,558,0,556,592,422,458,2,557,593,423,459,590,3,554,420,456,591,4,555,421,457,589,5,553,419,455,6,564,600,430,466,562,598,428,7,464,599,563,429,8,465,560,596,426,9,462,561,597,427,10,463,559,595,425,11,461,663,665,671,670,108,582,472,262,606,109,604,580,470,263,110,605,581,471,261,578,107,602,468,265,579,105,603,469,266,577,106,601,467,264,114,612,588,478,268,610,586,476,115,269,587,611,477,116,267,608,584,474,113,271,609,585,475,111,272,607,583,473,112,270,679,682,686,688 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#b9c83ee29c9828886a1d9280722af908f3a23a39dfe3e8d4571f7572270a5310, 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 20:06:55 · history