Equation 677 Database

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Magma 345d99c5b651…

magma 345d99c5b651
Size
595
Isomorphism class hash
345d99c5b65145e124e54235a368d2239d80d0c5426b887ca551afc18b658df7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 17:47:35
Display reorder
307,306,308,309,310,311,75,74,76,77,72,73,377,379,378,382,380,381,397,399,398,401,402,400,350,352,351,349,347,348,513,525,527,550,594,263,259,258,261,262,260,31,30,32,33,34,35,224,223,225,226,227,222,64,63,65,60,61,62,44,43,45,46,47,42,186,191,187,188,189,190,56,55,57,58,59,54,0,1,2,3,4,5,94,93,95,90,91,92,123,122,124,125,120,121,359,361,360,362,363,364,324,323,322,319,320,321,338,340,339,341,342,343,396,395,394,392,393,391,481,482,506,505,479,480,344,464,435,466,436,465,521,533,529,531,519,514,576,559,548,544,569,551,545,574,573,584,23,19,18,21,22,20,170,169,171,172,173,168,101,100,96,97,98,99,160,159,161,156,157,158,141,140,142,143,138,139,149,148,144,145,146,147,264,269,265,266,267,268,136,135,137,132,133,134,240,245,241,242,243,244,28,27,29,24,25,26,454,453,418,493,499,492,490,500,491,488,489,487,509,495,501,494,456,455,486,451,450,447,446,444,409,411,410,408,406,407,346,470,439,471,440,472,541,534,540,510,511,539,562,560,565,566,563,561,585,547,591,543,102,104,103,106,107,105,175,174,176,177,178,179,87,86,88,89,84,85,235,234,236,237,238,239,213,212,214,215,210,211,40,39,41,36,37,38,183,182,184,185,180,181,66,71,67,68,69,70,232,231,233,228,229,230,288,293,289,290,291,292,371,373,372,374,375,376,388,390,389,386,387,385,353,355,354,356,357,358,370,369,368,366,367,365,484,485,508,412,507,483,474,384,475,504,473,383,536,535,517,516,518,530,553,575,580,568,552,546,577,590,578,556,286,282,287,284,285,283,152,151,153,154,155,150,208,207,209,204,205,206,109,108,110,111,112,113,247,246,248,249,250,251,276,281,277,278,279,280,165,164,166,167,162,163,83,78,81,82,79,80,130,129,131,126,127,128,13,12,14,15,16,17,478,449,448,405,403,404,335,334,336,333,331,332,413,415,414,416,417,452,459,497,419,496,457,458,317,316,318,313,314,315,422,420,502,498,503,421,520,532,523,522,542,512,572,582,571,564,588,554,567,555,586,589,118,114,119,116,117,115,272,271,273,274,275,270,253,252,254,255,256,257,51,50,52,53,48,49,8,7,9,10,11,6,295,294,296,297,298,299,301,300,302,303,304,305,219,218,220,221,216,217,201,200,202,203,198,199,192,197,193,194,195,196,477,445,443,441,442,476,460,423,424,312,425,461,429,431,430,426,427,428,432,462,337,463,433,434,328,330,329,327,325,326,345,467,437,469,438,468,537,538,515,524,526,528,583,557,549,587,592,581,593,570,579,558 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#51f9b7d09d33f9fd9b24ec352fcf17309682f23da1a55124c3f963e5739f1055, M = the submagma generated by {12, 24} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 17:47:36 · history