Equation 677 Database

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Magma 10ec497010bc…

magma 10ec497010bc
Size
705
Isomorphism class hash
10ec497010bc30599ea97f4050faf3b0d4cdb0f67a23f75b29e80004a55f3cfe
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 16:00:02
Display reorder
660,70,577,560,575,573,595,597,71,581,593,555,557,69,540,553,637,66,620,635,633,641,67,657,655,653,68,617,600,615,613,537,521,61,535,533,497,481,62,495,493,517,501,60,515,513,449,440,64,448,447,477,461,65,475,473,420,437,63,435,433,700,702,696,703,162,568,576,566,570,586,588,163,596,590,546,548,164,556,550,628,165,636,626,630,656,166,648,646,650,167,608,616,606,610,528,536,160,526,530,488,496,161,486,490,508,516,159,506,510,455,457,156,442,444,468,476,157,466,470,436,428,158,426,430,688,694,692,690,215,403,245,294,101,295,404,213,243,99,296,402,214,244,100,406,211,241,297,97,242,212,407,298,98,210,405,240,299,96,401,251,206,292,107,399,249,204,293,105,400,250,205,291,106,397,247,209,288,103,398,248,207,289,104,246,396,208,290,102,664,666,683,676,180,286,82,270,391,271,287,181,83,392,272,285,182,81,390,282,183,78,273,394,79,184,283,274,395,185,284,80,275,393,277,73,186,268,389,278,74,187,269,387,276,72,188,267,388,280,76,189,264,385,281,77,190,265,386,75,279,191,266,384,684,677,671,668,146,569,572,564,567,584,589,144,592,587,544,549,145,552,547,629,149,632,624,627,652,147,649,644,647,148,609,612,604,607,529,532,152,524,527,489,492,150,484,487,509,512,151,504,507,443,446,155,452,454,469,472,153,464,467,432,429,154,424,427,699,697,704,686,0,574,562,565,563,585,594,2,582,583,545,554,1,542,543,634,4,622,625,623,642,5,654,645,643,3,614,602,605,603,534,522,7,525,523,494,482,8,485,483,514,502,6,505,503,456,450,10,453,451,474,462,11,465,463,422,434,9,425,423,687,691,695,698,55,578,579,561,571,580,598,56,599,591,541,558,54,559,551,638,58,639,621,631,659,59,658,640,651,57,618,619,601,611,539,538,53,520,531,499,498,51,480,491,519,518,52,500,511,459,458,49,441,445,479,478,50,460,471,438,439,48,421,431,689,685,693,701,193,135,415,121,118,122,136,194,416,119,120,137,192,414,117,134,196,418,124,114,419,197,132,125,115,195,133,417,123,116,141,413,199,127,109,142,411,200,128,110,143,412,198,126,108,140,409,202,130,112,138,410,203,131,113,408,139,201,129,111,678,679,681,672,259,216,231,307,86,308,217,260,232,84,306,218,258,233,85,219,262,230,310,89,228,263,220,311,87,261,221,229,309,88,222,237,257,305,92,223,238,255,303,90,224,239,256,304,91,225,236,253,301,95,226,234,254,302,93,235,227,252,300,94,663,661,675,670,177,328,367,355,379,356,329,178,368,380,354,327,179,366,378,324,176,370,358,382,371,174,325,359,383,175,326,369,357,381,334,365,168,353,377,335,363,169,351,375,333,364,170,352,376,330,361,171,349,373,331,362,172,350,374,360,332,173,348,372,665,667,669,674,340,34,18,37,317,38,35,341,19,315,36,33,339,20,316,30,336,21,40,313,22,337,31,41,314,338,32,23,39,312,25,16,346,43,323,26,17,347,44,321,24,15,345,42,322,28,12,342,46,319,29,13,343,47,320,14,27,344,45,318,682,673,662,680 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#2c9cca33fbeafeb683cb8962a04870775a8e5c306e9c00d15364712f8c215d93, 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 16:00:03 · history