Equation 677 Database

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Magma 5bf458b7a9cc…

magma 5bf458b7a9cc
Size
381
Isomorphism class hash
5bf458b7a9cccc9ca7c339d93cf5f70d8090a0be26b61035d8837fd32f043fb4
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 23:33:57
Display reorder
380,145,144,146,147,148,149,287,296,247,257,267,277,154,155,150,151,152,153,140,141,142,143,138,139,166,167,162,163,164,165,218,228,238,188,198,208,325,326,327,328,329,324,268,278,288,297,248,258,135,136,137,132,133,134,197,207,217,227,237,187,160,159,161,156,157,158,354,356,355,366,353,378,352,367,377,331,114,119,115,116,117,118,285,299,245,255,265,275,111,112,113,108,109,110,87,88,89,84,85,86,74,75,76,77,72,73,211,221,231,180,190,201,305,301,300,302,303,304,260,270,280,291,240,250,92,93,94,95,90,91,195,205,215,225,235,185,81,80,82,83,78,79,351,344,345,364,350,371,346,361,375,347,11,10,6,7,8,9,284,294,244,254,264,274,1,0,2,3,4,5,103,104,105,106,107,102,29,24,25,26,27,28,216,226,236,186,196,206,315,316,317,312,313,314,266,276,286,295,246,256,100,101,96,97,98,99,194,204,214,224,234,184,31,30,32,33,34,35,332,337,336,362,330,376,349,369,374,348,174,179,175,176,177,178,282,292,242,252,262,272,171,172,173,168,169,170,20,21,22,23,18,19,124,125,120,121,122,123,213,223,233,183,193,203,308,309,310,311,306,307,263,273,283,293,243,253,15,16,17,12,13,14,192,202,212,222,232,182,130,129,131,126,127,128,358,335,359,363,357,373,334,365,372,333,49,48,50,51,52,53,281,290,241,251,261,271,58,59,54,55,56,57,44,45,46,47,42,43,70,71,66,67,68,69,219,229,239,189,199,209,320,321,322,323,318,319,269,279,289,298,249,259,39,40,41,36,37,38,191,200,210,220,230,181,64,63,65,60,61,62,341,343,342,360,340,379,339,368,370,338 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 = {72} 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 23:33:57 · history