Equation 677 Database

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Magma 21a5bafb7a15…

magma 21a5bafb7a15
Size
705
Isomorphism class hash
21a5bafb7a1532c416c407c40826e90bb882b31b33341aaf9c64e20f1dcda26d
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 18:24:49
Display reorder
660,254,454,444,449,450,252,470,474,464,469,425,423,253,426,432,510,257,514,503,509,530,255,534,523,529,490,256,494,483,489,260,573,578,565,571,593,598,585,258,591,553,558,545,259,551,638,633,625,263,631,658,653,645,261,651,618,613,605,262,611,686,696,698,690,22,451,445,455,440,23,460,471,465,475,424,420,21,428,435,500,18,511,505,515,521,19,531,525,535,480,20,491,485,495,13,560,574,566,579,580,594,586,14,599,541,554,546,12,559,634,621,626,16,639,654,640,646,17,659,614,601,606,15,619,689,702,693,697,69,409,265,349,325,70,326,410,266,350,408,324,71,264,348,328,68,412,268,352,329,66,413,269,353,327,67,411,267,351,60,331,415,271,355,332,416,272,61,356,330,414,270,62,354,418,334,274,63,358,419,335,275,64,359,417,333,273,65,357,661,671,682,668,125,289,373,177,361,123,362,290,374,178,288,360,124,372,179,364,121,292,376,176,365,122,293,377,174,363,120,291,375,175,131,367,295,379,168,368,296,380,129,169,366,294,378,130,170,298,370,382,127,171,299,371,383,128,172,297,369,381,126,173,673,681,664,672,28,453,459,457,441,29,461,473,479,477,434,427,27,439,436,504,24,513,519,516,524,25,533,539,538,484,26,493,499,496,34,562,577,575,572,582,597,595,35,592,542,557,555,33,552,637,622,635,30,632,657,642,655,31,652,617,602,615,32,612,685,688,695,700,38,458,448,452,456,36,476,478,468,472,438,437,37,431,433,517,41,518,508,512,536,39,537,528,532,497,40,498,488,492,44,561,570,569,576,581,590,589,42,596,540,550,549,43,556,630,620,629,47,636,650,641,649,45,656,610,600,609,46,616,704,692,687,694,51,446,443,442,447,52,467,466,463,462,429,430,53,422,421,507,50,506,502,501,527,48,526,522,520,487,49,486,482,481,57,568,567,564,563,588,587,584,58,583,548,547,544,59,543,627,628,624,56,623,647,648,644,54,643,607,608,604,55,603,699,701,691,703,81,301,209,385,337,82,338,302,207,386,300,336,83,208,384,340,80,304,205,388,341,78,305,206,389,339,79,303,204,387,72,343,307,215,391,344,308,213,73,392,342,306,214,74,390,310,346,211,75,394,311,347,212,76,395,309,345,210,77,393,676,679,666,669,6,313,245,228,277,7,278,314,243,229,312,276,8,244,230,280,9,316,241,231,281,10,317,242,232,279,11,315,240,233,4,283,319,251,234,284,320,249,5,235,282,318,250,3,236,322,286,247,1,237,323,287,248,0,238,321,285,246,2,239,665,677,670,663,104,139,167,146,116,102,114,140,165,144,138,115,103,166,145,119,107,142,163,149,117,105,143,164,147,118,106,141,162,148,99,111,137,158,152,112,135,156,100,150,113,136,157,101,151,133,110,161,98,155,134,108,159,96,153,132,109,160,97,154,662,683,675,667,90,397,191,226,193,91,194,398,189,227,396,192,92,190,225,196,93,400,187,222,197,94,401,188,223,195,95,399,186,224,88,199,403,182,217,200,404,180,89,218,198,402,181,87,216,406,202,185,84,220,407,203,183,85,221,405,201,184,86,219,674,678,680,684 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#82fe73547f12a148ba897be501ddca2fd72765d56930c9a3792aacda34cfdc1d, 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 18:24:50 · history