Equation 677 Database

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Magma 9c1152d568dc…

magma 9c1152d568dc
Size
705
Isomorphism class hash
9c1152d568dc32f32229ef25aa19693101d1ec5ac736ba9002f94b92649f8717
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 16:36:39
Display reorder
660,554,553,556,101,541,574,573,99,576,560,100,593,594,596,580,613,614,97,616,601,633,634,98,636,621,653,654,96,656,640,513,514,516,107,501,533,534,536,105,521,493,494,496,106,480,433,434,436,103,421,450,451,457,104,456,473,474,476,102,460,696,702,693,698,540,552,559,206,558,561,572,204,579,578,205,592,581,598,599,612,600,209,618,619,632,620,207,639,638,652,641,208,658,659,512,504,519,212,518,532,524,539,210,538,492,484,498,211,499,432,424,439,215,438,449,443,459,213,458,472,464,478,214,479,694,695,692,701,282,409,16,272,408,283,411,270,17,410,271,413,284,15,412,414,285,275,12,415,417,286,273,13,416,419,287,274,14,418,405,280,22,267,404,407,281,23,268,406,402,279,21,269,403,396,276,18,266,397,399,277,19,264,398,401,278,20,265,400,661,684,683,676,61,330,154,58,390,62,331,59,155,391,57,332,60,153,392,333,64,54,150,393,334,65,55,151,394,335,63,56,152,395,328,67,145,49,388,329,68,146,50,389,327,66,144,48,387,324,70,148,52,384,325,71,149,53,385,326,69,147,51,386,663,681,668,670,557,550,548,254,545,577,570,252,568,565,253,590,597,588,585,610,617,257,608,605,630,637,255,628,625,650,657,256,648,645,510,517,508,260,505,530,537,528,258,525,490,497,488,259,485,430,437,428,263,425,453,455,446,261,444,470,477,468,262,465,686,697,689,688,555,542,546,82,549,575,562,83,566,569,81,582,595,586,589,602,615,78,606,609,622,635,79,626,629,642,655,80,646,649,500,515,506,73,509,520,535,526,74,529,481,495,486,72,489,420,435,426,76,429,452,454,445,77,447,461,475,466,75,469,690,700,699,687,551,544,547,42,543,571,564,43,567,563,44,584,591,587,583,604,611,45,607,603,624,631,46,627,623,644,651,47,647,643,503,511,507,40,502,523,531,527,41,522,483,491,487,39,482,423,431,427,36,422,442,448,441,37,440,463,471,467,38,462,691,703,704,685,247,130,134,224,378,248,131,222,132,379,223,129,246,133,380,126,250,227,137,381,127,251,225,135,382,128,249,226,136,383,121,245,140,219,376,122,243,138,220,377,120,244,139,221,375,124,241,143,218,372,125,242,141,216,373,123,240,142,217,374,665,680,671,669,306,84,318,0,110,307,85,2,319,108,1,86,308,320,109,87,309,4,321,113,88,310,5,322,111,89,311,3,323,112,90,304,316,7,116,91,305,317,8,114,92,303,315,6,115,93,300,312,10,119,94,301,313,11,117,95,302,314,9,118,666,678,682,667,178,193,366,165,182,179,194,166,367,180,167,192,177,368,181,196,174,164,369,185,197,175,162,370,183,195,176,163,371,184,199,169,364,156,188,200,170,365,157,186,198,168,363,158,187,202,172,360,159,191,203,173,361,160,189,201,171,362,161,190,677,672,674,679,354,342,294,229,25,355,343,230,295,26,228,344,356,296,24,345,357,232,297,28,346,358,233,298,29,347,359,231,299,27,340,352,292,235,31,341,353,293,236,32,339,351,291,234,30,336,348,288,238,34,337,349,289,239,35,338,350,290,237,33,675,662,673,664 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#368900d303714df43b3718b8680935166fd1150994cfe143b7c0fba0a5b985be, 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 16:36:40 · history