Equation 677 Database

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Magma 7d29a1a13e6f…

magma 7d29a1a13e6f
Size
705
Isomorphism class hash
7d29a1a13e6f5eb66bad5e4a8e344d83ca80d4791d795d69a1d605e0ff33880d
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 15:33:17
Display reorder
704,454,431,433,272,455,270,429,434,430,271,453,432,450,427,275,436,451,428,273,437,452,426,274,435,445,439,422,267,446,440,420,268,444,438,421,269,442,448,425,266,443,449,423,264,441,447,424,265,412,413,411,408,409,410,418,419,416,414,415,417,675,673,672,674,497,522,535,51,495,52,523,536,524,53,496,534,493,525,50,538,494,526,48,539,492,527,49,537,503,533,520,57,501,531,521,58,502,532,519,59,529,499,516,56,530,500,517,54,528,498,518,55,513,514,515,512,510,511,504,505,509,507,508,506,664,666,667,665,17,281,295,67,15,68,279,296,280,66,16,294,13,277,70,298,14,278,71,299,12,276,69,297,23,293,287,65,21,291,285,63,22,292,286,64,289,19,283,61,290,20,284,62,288,18,282,60,648,649,650,651,652,653,654,655,658,656,657,659,686,684,687,685,133,109,131,107,134,105,110,129,108,106,132,130,136,112,103,127,137,113,104,128,135,111,102,126,139,122,115,98,140,120,116,96,138,121,114,97,125,142,118,101,123,143,119,99,124,141,117,100,152,150,151,155,153,154,147,148,145,146,144,149,701,703,702,700,589,625,647,157,590,158,626,645,624,156,588,646,592,628,160,643,593,629,161,644,591,627,159,642,595,638,631,163,596,636,632,164,594,637,630,162,641,598,634,166,639,599,635,167,640,597,633,165,463,464,462,466,467,465,461,459,456,457,458,460,689,691,690,688,313,337,358,7,314,8,338,359,336,6,312,357,316,340,10,354,317,341,11,355,315,339,9,356,319,349,343,5,320,350,344,3,318,348,342,4,352,322,346,0,353,323,347,2,351,321,345,1,331,332,330,334,335,333,329,327,324,325,326,328,662,661,660,663,186,211,173,479,187,477,212,171,210,478,188,172,189,214,475,169,190,215,476,170,191,213,474,168,184,179,209,470,185,177,207,468,183,178,208,469,175,180,205,473,176,181,206,471,174,182,204,472,201,202,203,200,198,199,192,193,197,195,196,194,694,693,692,695,87,620,74,302,88,300,618,72,619,301,89,73,86,623,305,77,84,621,303,75,85,622,304,76,93,80,615,308,94,78,616,306,95,79,617,307,83,92,614,311,81,90,612,309,82,91,613,310,609,610,611,608,606,607,600,601,605,603,604,602,682,683,680,681,217,249,262,491,218,489,250,263,251,490,216,261,220,248,487,258,221,246,488,259,219,247,486,260,223,253,240,482,224,254,241,480,222,252,242,481,256,226,243,485,257,227,244,483,255,225,245,484,236,234,235,239,237,238,231,232,229,230,228,233,696,698,697,699,546,570,584,39,547,40,571,582,572,41,548,583,549,573,38,587,550,574,36,585,551,575,37,586,544,579,568,45,545,580,569,46,543,581,567,47,578,540,564,44,576,541,565,42,577,542,566,43,561,562,563,560,558,559,552,553,557,555,556,554,671,668,669,670,366,390,402,29,367,27,391,403,392,28,368,404,369,393,25,405,370,394,26,406,371,395,24,407,364,400,388,35,365,401,389,33,363,399,387,34,396,360,384,31,397,361,385,32,398,362,386,30,381,382,383,380,378,379,372,373,377,375,376,374,676,678,679,677 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#200706f015266953205238906f67170c94edeebe72a54762b43b1258f263dcc8, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:33:19 · history