Equation 677 Database

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Magma 11dc4fd69409…

magma 11dc4fd69409
Size
381
Isomorphism class hash
11dc4fd69409df778f5a09e932ea4ff56a5934616bc9cf674dc17966a195920d
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 23:30:28
Display reorder
380,232,217,192,180,209,223,235,200,214,321,233,218,194,182,204,323,224,236,201,215,219,228,197,183,205,325,225,237,202,210,229,220,195,184,206,327,226,238,203,211,230,221,193,185,207,329,227,239,198,212,319,216,231,196,181,208,222,234,199,213,189,191,187,186,188,190,357,336,371,370,355,354,335,334,353,356,123,141,168,158,150,149,131,176,133,305,124,142,169,159,151,306,144,126,177,134,143,125,170,160,152,307,145,127,178,135,120,138,171,161,153,308,146,128,179,136,121,139,172,156,154,309,147,129,174,137,304,140,122,173,157,155,148,130,175,132,166,162,163,164,165,167,367,379,346,366,365,378,368,344,345,347,79,69,96,114,112,77,87,104,61,317,80,70,97,115,113,316,72,88,105,62,71,81,98,116,108,300,73,89,106,63,82,66,99,117,109,303,74,84,107,64,83,67,100,118,110,302,75,85,102,65,301,68,78,101,119,111,76,86,103,60,94,90,91,92,93,95,348,330,331,352,332,350,349,333,351,369,57,47,22,6,4,49,31,24,39,324,58,42,23,7,5,326,50,32,25,40,43,59,18,8,1,328,51,33,26,41,54,44,19,9,0,318,52,34,27,36,55,45,20,10,2,320,53,35,28,37,322,46,56,21,11,3,48,30,29,38,14,16,17,12,13,15,340,342,374,364,377,343,341,363,376,375,242,261,293,281,272,264,249,296,252,312,243,262,288,276,273,313,265,250,297,253,263,244,289,277,274,314,266,251,298,254,245,258,290,278,275,315,267,246,299,255,240,259,291,279,270,310,268,247,294,256,311,260,241,292,280,271,269,248,295,257,284,286,287,282,283,285,337,372,359,362,339,373,358,360,361,338 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#6947448508a963a3a65e3ca6e046f467db3b718f00faa1555f1fb34ed3ecdcf3, M = {66} 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 23:30:28 · history