Equation 677 Database

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Magma 5c73b4fcf9ef…

magma 5c73b4fcf9ef
Size
705
Isomorphism class hash
5c73b4fcf9efe2dd6b311709d80e563e6d42c7145339648e3cf9a8e109be8250
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 20:31:16
Display reorder
660,554,208,548,549,541,568,574,569,561,209,588,207,594,589,581,204,608,614,609,600,205,628,634,629,620,206,648,654,649,640,508,514,214,509,501,529,528,534,215,521,488,494,213,489,481,434,428,210,429,421,448,445,211,457,456,474,468,212,469,461,701,702,694,685,557,197,544,558,559,564,577,578,579,195,584,196,597,599,598,193,604,617,619,618,194,624,637,638,639,192,644,657,659,658,504,517,203,518,519,538,524,537,201,539,484,497,202,499,498,437,423,199,438,439,451,442,200,458,459,477,463,198,479,478,687,690,700,686,408,131,156,172,409,157,410,173,411,129,158,130,413,171,412,127,159,414,168,415,128,160,416,169,417,126,161,418,170,419,162,404,122,178,405,179,163,406,120,407,164,402,121,177,403,396,165,125,174,397,398,166,123,175,399,400,167,124,176,401,668,683,684,678,238,119,330,20,390,331,239,18,391,117,332,118,237,19,392,115,333,234,23,393,116,334,235,21,394,114,335,236,22,395,328,229,110,15,388,16,329,230,108,389,327,228,109,17,387,232,324,113,14,384,233,325,111,12,385,231,326,112,13,386,677,681,663,672,553,144,550,556,551,570,573,576,571,145,590,146,593,596,591,147,610,613,616,611,148,630,633,636,631,149,650,653,656,651,510,513,150,516,511,536,530,533,151,531,490,493,152,496,491,433,430,153,436,431,455,454,154,450,446,473,470,155,476,471,696,698,692,695,547,43,546,552,555,566,567,572,575,44,586,42,587,592,595,46,606,607,612,615,47,626,627,632,635,45,646,647,652,655,506,507,41,512,515,532,526,527,39,535,486,487,40,492,495,427,426,37,432,435,453,452,38,447,449,467,466,36,472,475,688,691,699,697,545,57,542,543,540,562,565,563,560,58,582,59,585,583,580,56,602,605,603,601,54,622,625,623,621,55,642,645,643,641,500,505,48,503,502,523,520,525,49,522,480,485,50,483,482,425,424,51,422,420,444,443,52,441,440,465,464,53,462,460,693,703,704,689,186,7,134,354,378,132,187,355,379,8,133,6,188,356,380,10,137,189,357,381,11,135,190,358,382,9,136,191,359,383,140,184,5,352,376,353,138,185,3,377,139,183,4,351,375,180,143,0,348,372,181,141,2,349,373,182,142,1,350,374,676,680,667,665,103,62,26,225,306,24,104,226,307,60,25,61,102,227,308,65,29,106,224,309,63,27,107,222,310,64,28,105,223,311,32,101,68,216,304,217,30,99,66,305,31,100,67,218,303,97,35,71,219,300,98,33,69,220,301,96,34,70,221,302,661,669,682,674,244,76,366,282,255,367,245,283,256,77,368,75,243,284,257,72,369,240,285,254,73,370,241,286,252,74,371,242,287,253,364,250,82,280,261,281,365,251,83,262,363,249,81,279,263,246,360,78,276,260,247,361,79,277,258,248,362,80,278,259,664,671,675,679,294,85,270,318,342,271,295,319,343,86,272,84,296,320,344,88,273,297,321,345,89,274,298,322,346,87,275,299,323,347,268,292,91,316,340,317,269,293,92,341,267,291,90,315,339,288,264,94,312,336,289,265,95,313,337,290,266,93,314,338,670,673,666,662 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#be22598f61f867b223264cf52ecf408910eea148415a700aef96392fba43b30a, 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 20:31:16 · history