Equation 677 Database

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Magma 03ff60f4ec18…

magma 03ff60f4ec18
Size
705
Isomorphism class hash
03ff60f4ec184d5dbb531376a5dfd8d2fb1f303c0878fe28a1c12b2bfddd3445
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 18:11:15
Display reorder
660,201,333,448,346,288,289,334,202,449,347,335,290,203,447,345,291,200,332,444,342,198,292,330,445,343,293,199,331,446,344,339,207,286,454,352,208,287,455,340,353,209,285,453,341,351,282,206,450,338,348,283,204,451,336,349,284,205,452,337,350,686,679,673,677,99,406,390,484,65,63,407,100,391,485,405,64,101,392,483,61,98,402,393,480,96,62,403,394,481,60,97,404,395,482,412,90,71,396,490,91,69,397,413,491,92,70,398,411,489,67,93,399,408,486,68,94,400,409,487,66,95,401,410,488,669,662,665,671,22,358,550,14,472,473,359,23,551,12,357,471,21,549,13,468,18,354,546,17,19,469,355,547,15,470,20,356,548,16,364,28,478,556,9,29,479,557,365,10,27,477,555,363,11,474,24,552,360,8,475,25,553,361,6,476,26,554,362,7,678,675,680,683,162,387,47,442,76,77,388,163,45,443,389,75,164,46,441,72,165,386,43,438,166,73,384,44,439,74,167,385,42,440,648,168,646,645,649,169,654,652,656,657,170,638,637,640,641,614,171,613,616,617,622,172,621,624,625,630,173,628,632,633,703,699,704,700,192,496,305,221,418,419,497,193,303,219,495,417,194,304,220,414,195,492,301,217,196,415,493,302,218,416,197,494,300,216,502,190,424,296,212,191,425,294,503,210,189,423,295,501,211,420,186,299,498,215,421,187,297,499,213,422,188,298,500,214,690,693,692,689,269,127,125,538,460,461,128,267,123,539,126,459,268,124,537,456,265,130,121,534,266,457,131,122,535,458,264,129,120,536,133,260,466,116,544,258,467,114,134,545,259,465,115,132,543,462,263,119,136,540,463,261,117,137,541,464,262,118,135,542,663,667,668,661,311,430,146,233,235,236,431,309,144,231,429,234,310,145,232,238,307,426,149,229,308,239,427,147,230,237,306,428,148,228,436,317,241,141,224,315,242,142,437,222,316,240,143,435,223,244,313,140,432,227,245,314,138,433,225,243,312,139,434,226,695,691,696,694,257,604,318,106,586,587,605,255,319,107,603,585,256,320,105,582,253,600,321,102,254,583,601,322,103,584,252,602,323,104,610,248,592,324,112,246,593,325,611,113,247,591,326,609,111,588,251,327,606,108,589,249,328,607,109,590,250,329,608,110,685,688,682,674,151,2,598,532,381,382,1,152,599,533,0,383,150,597,531,380,154,5,594,528,155,378,3,595,529,379,153,4,596,530,644,157,647,651,650,158,655,659,653,658,156,639,643,636,642,618,160,619,612,615,623,161,627,620,626,631,159,635,629,634,697,698,701,702,185,508,89,53,574,575,509,183,87,51,507,573,184,88,52,570,181,504,85,49,182,571,505,86,50,572,180,506,84,48,514,176,580,80,59,174,581,78,515,57,175,579,79,513,58,576,179,83,510,55,577,177,81,511,56,578,178,82,512,54,670,666,672,664,41,370,520,562,279,280,371,39,521,563,369,281,40,519,561,278,37,366,516,558,38,276,367,517,559,277,36,368,518,560,376,32,270,526,568,30,271,527,377,569,31,272,525,375,567,273,35,522,372,564,274,33,523,373,565,275,34,524,374,566,687,676,684,681 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#6997491de262e367994a4a50c6f8055cb54c2a6a0260cea123f554e749c551e0, 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 18:11:16 · history