Equation 677 Database

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Magma a42bbe685da2…

magma a42bbe685da2
Size
705
Isomorphism class hash
a42bbe685da2fdc11c1a43ec875db45ccd99134e6e82ce0cdeb9838c561f7c3f
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 15:12:47
Display reorder
660,525,538,21,529,531,485,498,22,489,491,505,23,509,511,518,455,447,20,449,450,475,464,18,467,468,435,424,19,427,428,645,658,649,12,651,605,618,609,13,611,14,625,638,629,631,578,565,569,15,571,598,585,589,16,591,558,545,549,17,551,696,691,686,701,526,536,191,522,523,486,496,189,482,483,506,190,502,503,516,453,443,187,441,442,473,465,188,462,463,433,425,186,422,423,646,656,642,182,643,606,616,602,180,603,181,626,636,622,623,576,566,562,185,563,596,586,582,183,583,556,546,542,184,543,700,688,689,697,151,281,158,128,81,152,279,156,126,82,150,157,127,83,280,277,154,161,131,80,278,155,159,129,78,276,153,160,130,79,149,287,123,164,72,147,285,124,162,73,163,148,286,125,74,283,145,122,167,75,284,146,120,165,76,282,144,121,166,77,674,666,670,664,401,8,54,389,115,399,6,55,387,116,400,56,388,114,7,11,397,57,385,118,9,398,58,386,119,10,396,59,384,117,407,3,395,52,113,405,4,393,53,111,51,406,5,394,112,2,403,391,48,109,1,404,392,49,110,0,402,390,50,108,681,675,682,683,521,530,133,532,534,480,490,134,492,494,501,132,512,514,510,456,448,136,451,452,478,460,137,469,471,436,421,135,429,431,640,650,652,139,654,601,610,612,140,614,138,620,630,632,634,570,561,572,142,574,590,581,592,143,594,550,540,552,141,554,692,703,694,702,524,537,29,527,539,484,497,27,487,499,504,28,507,519,517,454,458,25,457,459,474,477,26,476,479,434,438,24,437,439,644,657,647,35,659,604,617,607,33,619,34,624,637,627,639,577,564,567,31,579,597,584,587,32,599,557,544,547,30,559,685,690,698,699,533,528,45,520,535,493,488,46,481,495,513,47,500,515,508,444,445,44,440,446,466,470,42,461,472,426,430,43,420,432,653,648,641,36,655,613,608,600,37,615,38,633,628,621,635,568,573,560,39,575,588,593,580,40,595,548,553,541,41,555,704,695,693,687,269,377,202,257,247,267,375,203,255,248,268,201,256,246,376,373,265,198,253,250,374,266,199,254,251,372,264,200,252,249,275,383,263,193,245,273,381,261,194,243,192,274,382,262,244,379,271,259,196,241,380,272,260,197,242,378,270,258,195,240,661,680,663,678,317,413,71,106,238,315,411,69,107,239,316,70,105,237,412,409,313,67,102,234,410,314,68,103,235,408,312,66,104,236,323,419,97,62,229,321,417,98,60,230,61,322,418,96,228,415,319,100,65,232,416,320,101,63,233,414,318,99,64,231,672,679,668,684,341,293,175,329,353,339,291,176,327,351,340,174,328,352,292,289,337,178,325,349,290,338,179,326,350,288,336,177,324,348,347,299,335,173,359,345,297,333,171,357,172,346,298,334,358,295,343,331,169,355,296,344,332,170,356,294,342,330,168,354,669,676,673,665,220,206,89,305,365,221,204,87,303,363,219,88,304,364,205,209,216,85,301,361,207,217,86,302,362,208,218,84,300,360,226,212,311,95,371,227,210,309,93,369,94,225,211,310,370,215,222,307,91,367,213,223,308,92,368,214,224,306,90,366,667,677,671,662 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#0afaa5a95ac3a042540e79b2adb5184e36490c06a1d05440665a030a584e7e24, 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 15:12:48 · history