Equation 677 Database

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Magma bb6007a20b1d…

magma bb6007a20b1d
Size
381
Isomorphism class hash
bb6007a20b1d30b50efed512556e9af08d2589bbe1a56d8b6f43fd51434fe1fe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:33:48
Display reorder
380,324,329,325,326,327,328,219,237,249,264,279,294,149,164,179,194,209,134,0,2,3,4,5,1,144,159,174,189,204,129,10,11,6,7,8,9,88,89,84,85,86,87,273,288,214,228,243,258,254,269,284,299,224,235,168,183,198,123,138,153,94,93,95,90,91,92,364,346,357,350,368,347,379,331,374,332,316,315,317,312,313,314,213,227,242,257,272,287,139,154,169,184,199,124,63,64,65,60,61,62,137,152,167,182,197,122,66,67,68,69,70,71,34,35,30,31,32,33,278,293,210,236,248,263,244,259,274,289,215,229,173,188,203,128,143,158,27,26,28,29,24,25,353,336,361,354,373,335,369,342,367,343,300,301,302,303,304,305,211,226,241,256,271,285,146,161,176,191,206,131,79,80,81,82,83,78,136,150,165,180,195,121,74,75,76,77,72,73,97,98,99,100,101,96,277,292,218,232,247,262,251,266,281,296,221,238,172,187,202,127,142,157,102,107,103,104,105,106,356,337,351,363,372,348,376,345,366,344,319,318,320,321,322,323,217,231,246,261,276,291,145,160,175,190,205,130,19,20,21,22,23,18,141,156,171,186,201,126,14,15,16,17,12,13,53,48,49,50,51,52,275,290,216,230,245,260,250,265,280,295,220,233,170,185,200,125,140,155,57,56,58,59,54,55,355,340,362,352,370,341,375,334,371,333,308,307,309,310,311,306,223,234,253,268,283,298,147,162,177,192,207,132,110,111,112,113,108,109,148,163,178,193,208,133,115,116,117,118,119,114,47,42,43,44,45,46,270,286,212,225,240,255,252,267,282,297,222,239,166,181,196,120,135,151,38,37,39,40,41,36,358,339,360,359,365,338,377,330,378,349 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {70} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:33:49 · history