Equation 677 Database

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Magma a04c5ab0a11b…

magma a04c5ab0a11b
Size
399
Isomorphism class hash
a04c5ab0a11b29c03818c69f0bbbaac783d269eb8d414431cbe44500894d76f2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:54:19
Display reorder
142,143,135,136,137,138,139,140,141,126,127,128,129,130,131,132,133,134,381,26,144,74,117,75,18,145,118,19,146,76,119,20,147,77,120,21,78,121,148,22,149,79,122,23,150,80,123,24,151,72,124,25,152,73,125,153,83,35,110,154,84,27,111,155,85,28,112,156,86,29,113,157,87,30,114,158,88,31,115,159,89,32,116,160,81,33,108,161,82,34,109,392,386,385,391,253,2,299,333,300,254,3,334,255,4,301,335,256,5,302,336,257,303,337,6,258,7,304,338,259,8,305,339,260,1,297,340,252,0,298,341,11,292,262,326,12,293,263,327,13,294,264,328,14,295,265,329,15,296,266,330,16,288,267,331,17,289,268,332,9,290,269,324,10,291,261,325,384,390,389,383,237,170,306,281,307,238,162,282,239,163,308,283,240,164,309,284,241,310,285,165,242,166,311,286,234,167,312,287,235,168,313,279,236,169,314,280,179,315,246,274,171,316,247,275,172,317,248,276,173,318,249,277,174,319,250,278,175,320,251,270,176,321,243,271,177,322,244,272,178,323,245,273,387,398,397,388,91,221,349,342,351,92,222,344,93,223,353,346,94,224,355,348,95,357,350,216,96,217,359,352,97,218,343,354,98,219,345,356,90,220,347,358,230,367,100,360,231,369,101,362,232,371,102,364,233,373,103,366,225,375,104,368,226,376,105,370,227,361,106,372,228,363,107,374,229,365,99,377,393,395,396,394,55,46,196,199,197,56,47,200,57,48,189,201,58,49,190,202,59,191,203,50,60,51,192,204,61,52,193,205,62,53,194,206,54,45,195,198,39,180,64,208,40,181,65,209,41,182,66,210,42,183,67,211,43,184,68,212,44,185,69,213,36,186,70,214,37,187,71,215,38,188,63,207,380,382,379,378 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#6adf7186d9fa6fa8b1a70500bdeeeb81c4a3cd4a94a239f0a46b26d1277fc3d6, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-06 19:54:20 · history