Equation 677 Database

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Magma 24fed39593b0…

magma 24fed39593b0
Size
399
Isomorphism class hash
24fed39593b06284aebe1a302e723b3c24bfafddf71266fc2b4462723480453e
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
2026-10-07 15:32:30
Display reorder
159,160,161,153,154,155,156,157,158,152,144,145,146,147,148,149,150,151,381,180,125,169,137,181,117,138,170,182,118,162,139,183,119,163,140,184,120,164,141,185,121,165,142,186,122,166,143,187,123,167,135,188,124,168,136,189,178,109,130,190,179,110,131,191,171,111,132,112,192,172,133,193,173,113,134,194,174,114,126,195,175,115,127,196,176,116,128,197,177,108,129,392,386,385,391,298,217,263,333,299,218,334,264,300,219,265,335,301,220,266,336,302,221,267,337,303,222,268,338,304,223,269,339,305,224,261,340,297,216,262,341,291,256,226,326,292,257,227,327,293,258,228,328,229,294,259,329,295,260,230,330,296,252,231,331,288,253,232,332,289,254,233,324,290,255,225,325,384,390,389,383,92,306,209,245,93,307,246,210,94,308,211,247,95,309,212,248,96,310,213,249,97,311,214,250,98,312,215,251,90,313,207,243,91,314,208,244,101,202,315,238,102,203,316,239,103,204,317,240,318,104,205,241,105,206,319,242,106,198,320,234,107,199,321,235,99,200,322,236,100,201,323,237,387,398,397,388,13,273,349,342,14,274,344,351,15,275,353,346,16,276,355,348,17,277,357,350,9,278,359,352,10,270,343,354,11,271,345,356,12,272,347,358,6,367,282,360,7,369,283,362,8,371,284,364,285,1,373,366,0,375,286,368,2,376,287,370,3,361,279,372,4,363,280,374,5,365,281,377,393,395,396,394,61,72,31,50,62,73,51,32,54,74,33,52,55,75,34,53,56,76,35,45,57,77,27,46,58,78,28,47,59,79,29,48,60,80,30,49,70,24,81,43,71,25,82,44,63,26,83,36,84,64,18,37,65,19,85,38,66,20,86,39,67,21,87,40,68,22,88,41,69,23,89,42,380,382,379,378 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#721593744294d1961397fd7afc0837ccff35badac9dfa1b01fcfd358557fdc12, 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 2026-10-07 15:32:32 · history