Equation 677 Database

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Magma 163e3768f45d…

magma 163e3768f45d
Size
705
Isomorphism class hash
163e3768f45d11774be6fc9265936aa241f48847b8f63d743ed6b7979e3ea76f
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 17:29:37
Display reorder
660,279,553,547,557,558,280,573,577,578,567,281,593,587,597,598,613,278,607,617,618,633,276,627,637,638,653,277,647,657,658,285,513,507,517,518,286,533,527,537,538,287,493,487,497,498,284,425,422,427,428,282,452,446,455,456,283,472,466,475,476,696,699,687,689,133,548,554,556,559,134,568,576,579,574,132,588,594,596,599,608,136,614,616,619,628,137,634,636,639,648,135,654,656,659,139,508,514,516,519,140,528,534,536,539,138,488,494,496,499,142,434,437,426,429,143,447,453,454,457,141,467,473,474,477,693,702,692,691,56,190,390,63,108,54,191,64,109,391,55,189,392,65,110,186,59,393,62,111,187,57,394,60,112,188,58,395,61,113,51,181,388,69,114,52,182,389,70,115,53,180,387,71,116,50,184,384,68,117,48,185,385,66,118,49,183,386,67,119,663,662,667,680,20,366,402,212,258,18,367,210,259,403,19,368,404,211,260,369,23,405,215,261,370,21,406,213,262,371,22,407,214,263,15,364,400,207,256,16,365,401,208,257,17,363,399,209,255,14,360,396,206,252,12,361,397,204,253,13,362,398,205,254,674,661,677,681,128,540,541,546,545,126,560,566,565,561,127,581,580,586,585,600,131,601,606,605,620,129,621,626,625,641,130,640,646,645,123,501,500,506,505,124,521,520,526,525,125,481,480,486,485,122,420,421,433,432,120,441,440,445,444,121,461,460,465,464,695,704,700,697,264,543,544,549,550,265,563,569,570,564,266,583,584,589,590,603,267,604,609,610,623,268,624,629,630,643,269,644,649,650,270,503,504,509,510,271,523,524,529,530,272,483,484,489,490,273,430,431,435,436,274,442,443,448,449,275,462,463,468,469,698,701,703,694,219,555,542,552,551,220,575,572,571,562,221,595,582,592,591,615,218,602,612,611,635,216,622,632,631,655,217,642,652,651,225,515,502,512,511,226,535,522,532,531,227,495,482,492,491,224,438,439,424,423,222,459,458,451,450,223,478,479,471,470,688,685,690,686,7,150,99,330,342,8,151,331,343,100,6,152,101,332,344,153,10,98,333,345,154,11,96,334,346,155,9,97,335,347,5,148,105,328,340,3,149,106,329,341,4,147,107,327,339,0,144,104,324,336,2,145,102,325,337,1,146,103,326,338,670,672,665,675,43,247,295,83,169,44,248,81,170,296,42,246,294,82,168,250,46,298,79,172,251,47,299,80,173,249,45,297,78,171,41,245,293,74,175,39,243,291,72,176,40,244,292,73,174,37,241,289,77,178,38,242,290,75,179,36,240,288,76,177,679,684,671,669,25,414,378,197,354,26,415,195,355,379,24,416,380,196,356,417,28,381,193,357,418,29,382,194,358,419,27,383,192,359,31,412,376,203,352,32,413,377,201,353,30,411,375,202,351,34,408,372,199,348,35,409,373,200,349,33,410,374,198,350,683,676,682,678,90,158,228,318,306,91,156,319,307,229,92,157,230,320,308,161,93,231,321,309,159,94,232,322,310,160,95,233,323,311,88,164,234,316,304,89,162,235,317,305,87,163,236,315,303,84,167,237,312,300,85,165,238,313,301,86,166,239,314,302,668,664,666,673 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#58222ccd0574e7adf03b9b32a848bfc3e464df8d7127a3e76f96a819fe65341a, 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 17:29:38 · history