Equation 677 Database

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Magma 1355701a5457…

magma 1355701a5457
Size
705
Isomorphism class hash
1355701a54578fdbe709ee66887208cd8ae77b67bf64edaaae3da1f8c0f34522
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 19:57:05
Display reorder
660,69,406,526,185,454,527,70,183,455,407,525,71,405,184,453,522,68,402,181,450,403,66,523,182,451,524,67,404,180,452,397,517,191,60,445,398,518,189,61,446,396,516,190,62,444,520,400,187,63,448,521,401,188,64,449,65,519,399,186,447,674,683,686,681,238,292,310,11,334,311,239,9,335,293,309,237,291,10,333,306,234,288,7,330,289,235,307,8,331,308,236,290,6,332,298,301,2,229,325,299,302,1,230,326,297,300,0,228,324,304,294,5,232,328,305,295,3,233,329,231,303,296,4,327,670,663,662,666,75,247,466,19,370,467,76,20,371,248,465,77,246,18,369,462,74,250,22,366,251,72,463,23,367,464,73,249,21,368,245,457,17,81,361,243,458,15,82,362,244,456,16,83,360,460,241,13,80,364,461,242,14,78,365,79,459,240,12,363,688,678,684,679,168,645,644,646,651,652,169,654,659,653,637,170,636,638,643,612,167,613,614,619,620,165,621,622,627,629,166,628,630,635,97,172,178,159,594,98,173,176,160,592,96,171,177,161,593,596,597,598,162,600,604,605,606,163,611,164,174,175,179,595,697,704,700,698,120,418,196,562,478,197,121,563,479,419,195,122,417,561,477,192,119,414,558,474,415,117,193,559,475,194,118,416,560,476,409,202,553,111,469,410,203,554,112,470,408,201,552,113,468,198,412,556,114,472,199,413,557,115,473,116,200,411,555,471,695,692,689,690,25,514,382,270,590,383,26,271,591,515,381,24,513,272,589,378,28,510,273,586,511,29,379,274,587,380,27,512,275,588,505,373,268,31,581,506,374,269,32,582,504,372,267,30,580,376,508,264,34,584,377,509,265,35,585,33,375,507,266,583,667,672,665,669,218,574,134,430,140,132,219,431,138,575,133,217,573,429,139,130,214,570,426,136,571,215,131,427,137,129,216,572,428,135,565,125,421,209,146,566,123,422,210,144,564,124,420,208,145,128,568,424,212,142,126,569,425,213,143,211,127,567,423,141,691,693,694,696,93,442,262,394,538,263,94,395,539,443,261,95,441,393,537,258,92,438,390,534,439,90,259,391,535,260,91,440,392,536,433,253,385,84,529,434,254,386,85,530,432,252,384,86,528,256,436,388,87,532,257,437,389,88,533,89,255,435,387,531,680,687,673,682,58,647,648,649,650,656,59,657,658,655,640,57,639,641,642,616,54,615,617,618,623,55,624,625,626,632,56,631,633,634,206,223,226,49,577,207,221,227,50,578,205,222,225,48,576,602,601,603,52,599,608,607,609,53,610,51,220,204,224,579,703,701,699,702,104,502,157,346,550,158,102,347,551,503,156,103,501,345,549,153,100,498,342,546,499,101,154,343,547,155,99,500,344,548,493,148,337,110,541,494,149,338,108,542,492,147,336,109,540,151,496,340,106,544,152,497,341,107,545,105,150,495,339,543,664,671,661,668,45,490,358,322,286,359,46,323,287,491,357,47,489,321,285,354,44,486,318,282,487,42,355,319,283,356,43,488,320,284,481,349,313,36,277,482,350,314,37,278,480,348,312,38,276,352,484,316,39,280,353,485,317,40,281,41,351,483,315,279,676,675,677,685 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#b7ef46c52e3181531ee451cc516c519f12d29148a838b2a4381cb7ae279fb33d, 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 19:57:06 · history