Equation 677 Database

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Magma 88c14ec78d03…

magma 88c14ec78d03
Size
381
Isomorphism class hash
88c14ec78d03230f321c433c7f8558f06b6a7277a6b8df3990657d7e2dbb9762
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 23:21:45
Display reorder
380,6,206,106,120,221,20,35,135,236,30,130,230,201,0,50,101,16,116,215,241,41,91,196,226,26,125,211,10,110,321,245,323,318,95,319,146,322,256,155,170,271,285,186,181,280,151,265,165,291,175,276,161,260,295,45,56,70,85,80,251,66,141,76,60,320,190,340,341,349,343,351,342,377,361,370,367,8,208,108,123,223,23,38,138,238,33,133,233,203,3,53,103,18,118,218,243,43,93,198,228,28,128,213,13,113,329,249,325,326,99,327,149,324,259,158,173,273,288,188,183,283,153,268,168,293,178,278,163,263,298,49,58,73,88,83,253,68,143,78,63,328,193,358,356,344,348,330,350,379,364,374,368,5,205,105,121,220,21,36,136,235,32,132,232,200,1,51,100,15,115,216,240,40,90,195,225,25,126,210,11,111,306,246,308,309,96,310,145,307,255,156,171,270,286,185,182,282,150,266,166,290,176,275,160,261,296,46,55,71,86,82,250,65,140,75,61,311,191,355,345,333,353,334,354,376,362,371,366,9,209,109,122,222,22,39,139,239,34,134,234,204,4,54,104,19,119,219,244,44,94,199,229,29,129,214,14,114,303,248,305,301,98,300,148,304,258,159,172,272,289,189,184,284,154,269,169,294,179,279,164,264,299,48,59,72,89,84,254,69,144,79,64,302,194,359,347,346,338,337,339,378,363,373,369,7,207,107,124,224,24,37,137,237,31,131,231,202,2,52,102,17,117,217,242,42,92,197,227,27,127,212,12,112,316,247,312,313,97,314,147,317,257,157,174,274,287,187,180,281,152,267,167,292,177,277,162,262,297,47,57,74,87,81,252,67,142,77,62,315,192,332,331,335,336,357,352,375,360,372,365 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {76} 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 23:21:46 · history