Equation 677 Database

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Magma e3742f1ccb80…

magma e3742f1ccb80
Size
705
Isomorphism class hash
e3742f1ccb80279040172b04407233cff4e99b117ba4ca9ad1e99cc57a11585a
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 18:12:56
Display reorder
660,527,524,523,22,522,487,484,23,483,482,507,504,21,503,502,450,449,18,448,447,464,466,19,463,462,424,426,20,421,423,647,644,643,13,642,607,604,603,14,602,627,624,623,12,622,567,564,563,16,562,587,584,583,17,582,547,544,543,15,542,687,690,701,685,531,525,529,70,520,491,485,71,489,480,511,505,69,509,500,452,442,66,443,440,465,470,67,468,461,425,430,68,428,420,651,645,649,61,641,611,605,609,62,601,631,625,629,60,621,571,565,569,64,561,591,585,589,65,581,551,545,549,63,541,688,686,703,691,341,189,176,44,197,339,190,42,174,195,340,191,43,175,196,337,188,47,179,193,186,338,45,177,194,187,336,46,178,192,347,180,171,39,203,345,181,172,40,201,346,182,173,41,202,343,183,170,38,199,344,184,168,36,200,342,185,169,37,198,678,664,668,682,365,389,127,102,258,363,387,103,128,259,364,388,104,126,260,361,385,105,130,261,386,362,106,131,262,384,360,107,129,263,371,395,125,100,256,369,393,123,101,257,370,394,124,99,255,367,391,121,96,252,368,392,122,97,253,366,390,120,98,254,675,679,671,677,535,538,528,48,536,495,498,49,488,496,515,518,50,508,516,456,455,51,451,454,475,478,52,467,473,435,436,53,427,433,655,658,648,54,656,615,618,608,55,616,635,638,628,56,636,575,578,568,57,576,595,598,588,58,596,555,558,548,59,556,700,692,698,696,532,533,526,86,539,492,493,84,486,499,512,513,85,506,519,453,458,89,457,459,477,471,87,476,479,438,431,88,437,439,652,653,646,92,659,612,613,606,90,619,632,633,626,91,639,572,573,566,95,579,592,593,586,93,599,552,553,546,94,559,694,697,693,689,521,530,534,35,537,481,490,33,494,497,501,510,34,514,517,441,444,31,445,446,469,460,32,472,474,429,422,30,432,434,640,650,654,26,657,600,610,614,24,617,620,630,634,25,637,560,570,574,29,577,580,590,594,27,597,540,550,554,28,557,704,699,702,695,281,329,401,75,273,279,327,76,399,274,280,328,77,400,275,277,325,74,397,272,326,278,72,398,270,324,276,73,396,271,287,335,407,81,264,285,333,405,82,265,286,334,406,83,266,283,331,403,80,267,284,332,404,78,268,282,330,402,79,269,666,672,661,683,117,232,413,322,243,118,233,323,411,244,119,231,321,412,245,116,228,318,409,242,229,114,319,410,240,230,115,320,408,241,108,238,419,313,249,109,239,417,314,250,110,237,418,312,251,111,234,415,316,248,112,235,416,317,246,113,236,414,315,247,673,681,670,684,204,141,293,163,353,205,142,164,291,351,206,143,162,292,352,207,140,166,289,349,138,208,167,290,350,139,209,165,288,348,210,132,299,161,359,211,133,297,159,357,212,134,298,160,358,213,135,295,157,355,214,136,296,158,356,215,137,294,156,354,680,669,667,663,6,219,377,147,305,7,220,148,375,303,8,221,149,376,304,9,218,146,373,301,216,10,144,374,302,217,11,145,372,300,4,225,383,153,311,5,226,381,154,309,3,227,382,155,310,1,224,379,152,307,0,222,380,150,308,2,223,378,151,306,662,665,676,674 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#6b720d896a29843112ad3c0147d655cf7bb7a1ca51519c2978dbef59d093ebaf, 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 18:12:57 · history