Equation 677 Database

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Magma 330034f2fedc…

magma 330034f2fedc
Size
705
Isomorphism class hash
330034f2fedc636b8a5548f31e08b2cf7e35205bb759e175a31c5dfc12f4c5e1
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 19:49:43
Display reorder
704,419,206,426,436,204,417,427,437,205,418,428,435,415,209,429,432,416,207,430,433,414,208,431,434,212,424,410,442,210,425,408,443,211,423,409,441,420,215,413,438,421,213,411,439,422,214,412,440,402,403,404,405,406,407,400,401,398,396,397,399,674,673,675,672,581,33,596,554,34,579,594,552,35,580,595,553,577,32,599,557,578,30,597,555,576,31,598,556,24,591,587,560,25,592,585,558,26,593,586,559,590,27,583,563,588,28,584,561,589,29,582,562,569,567,568,565,566,564,575,573,570,571,572,574,666,664,667,665,234,185,245,55,183,235,243,56,184,236,244,54,237,181,241,58,238,182,242,59,239,180,240,57,191,251,232,53,189,249,233,51,190,250,231,52,247,187,228,49,248,188,229,50,246,186,230,48,648,649,650,651,652,653,654,655,658,656,657,659,685,687,684,686,71,108,80,93,109,69,78,94,110,70,79,95,67,111,83,92,68,112,81,90,66,113,82,91,114,75,62,84,115,76,60,85,116,77,61,86,74,117,65,87,72,118,63,88,73,119,64,89,97,98,96,100,101,99,103,104,105,106,107,102,700,703,701,702,491,223,448,461,224,489,449,459,222,490,447,460,487,226,444,457,488,227,445,458,486,225,446,456,221,454,482,467,219,455,480,465,220,453,481,466,450,217,485,463,451,218,483,464,452,216,484,462,474,475,476,477,478,479,472,473,470,468,469,471,688,691,689,690,316,41,329,343,39,317,327,344,40,315,328,342,312,37,325,346,313,38,326,347,314,36,324,345,47,335,322,341,45,333,323,339,46,334,321,340,331,43,318,337,332,44,319,338,330,42,320,336,300,301,302,303,304,305,306,307,311,309,310,308,662,660,663,661,529,122,498,509,120,530,499,507,121,528,500,508,532,125,501,505,533,123,502,506,531,124,503,504,128,496,535,515,126,497,536,513,127,495,534,514,492,131,538,511,493,129,539,512,494,130,537,510,524,522,523,527,525,526,519,520,517,518,516,521,694,692,695,693,284,199,297,258,200,282,298,259,198,283,299,260,287,202,296,261,285,203,294,262,286,201,295,263,197,288,279,256,195,289,280,257,196,290,281,255,291,193,278,252,292,194,276,253,293,192,277,254,267,268,269,266,264,265,273,274,271,272,270,275,681,683,680,682,165,548,170,136,546,166,168,137,547,167,169,135,164,551,173,132,162,549,171,133,163,550,172,134,543,176,156,142,544,174,157,143,545,175,158,141,179,542,159,138,177,540,160,139,178,541,161,140,148,149,147,144,145,146,154,155,152,150,151,153,697,696,699,698,629,16,642,602,17,627,643,600,15,628,644,601,625,12,645,605,626,13,646,603,624,14,647,604,22,640,635,608,23,641,633,606,21,639,634,607,636,18,631,611,637,19,632,609,638,20,630,610,617,615,616,613,614,612,623,621,618,619,620,622,671,669,670,668,372,8,385,357,6,373,386,358,7,374,384,359,375,11,388,356,376,9,389,354,377,10,387,355,3,391,378,348,4,392,379,349,5,390,380,350,394,2,381,351,395,1,382,352,393,0,383,353,361,362,360,364,365,363,367,368,369,370,371,366,676,679,677,678 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#adb39c7b26968070fd85ec3ca227f43c35cfd242a3390aaf8597bfe24e1ed89b, 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 19:49:44 · history