Equation 677 Database

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Magma 1806905cd33a…

magma 1806905cd33a
Size
381
Isomorphism class hash
1806905cd33af1be2cf7695b8e68edbd8983ae706cda9e5f2a05a4bbd5dff575
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 23:32:09
Display reorder
380,185,180,191,196,201,206,148,149,144,145,146,147,127,128,129,130,131,126,321,322,323,318,319,320,125,120,121,122,123,124,250,256,261,266,240,245,165,170,175,151,156,160,138,139,140,141,142,143,296,270,275,280,286,291,226,231,236,210,215,221,135,134,136,137,132,133,345,344,343,371,334,376,364,365,359,351,189,184,194,199,204,209,11,6,7,8,9,10,23,18,19,20,21,22,329,324,325,326,327,328,29,24,25,26,27,28,254,259,264,269,243,248,168,174,179,153,158,163,2,3,4,5,1,0,299,273,278,284,289,294,229,234,239,214,219,224,17,16,12,13,14,15,354,336,337,373,333,378,360,369,358,347,186,181,190,195,200,205,109,110,111,112,113,108,98,99,100,101,96,97,305,301,300,302,303,304,104,105,106,107,102,103,251,255,260,265,241,246,166,171,176,150,155,161,95,90,91,92,93,94,295,271,276,281,285,290,225,230,235,211,216,220,114,119,115,116,117,118,348,341,342,370,340,375,363,366,356,350,188,183,193,198,203,208,77,72,73,74,75,76,89,84,85,86,87,88,308,309,310,311,306,307,65,60,61,62,63,64,253,258,263,268,244,249,169,173,178,154,159,164,68,69,70,71,66,67,298,274,279,283,288,293,228,233,238,213,218,223,83,82,78,79,80,81,353,332,330,374,331,379,362,368,357,349,187,182,192,197,202,207,37,38,39,40,41,36,52,53,48,49,50,51,314,315,316,317,312,313,58,59,54,55,56,57,252,257,262,267,242,247,167,172,177,152,157,162,34,35,30,31,32,33,297,272,277,282,287,292,227,232,237,212,217,222,42,47,43,44,45,46,352,335,339,372,338,377,361,367,355,346 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {69} 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 23:32:10 · history