Equation 677 Database

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Magma c0ef679e084f…

magma c0ef679e084f
Size
381
Isomorphism class hash
c0ef679e084fe57f0f4c21ab80df4cbc8b9ad8f9d0e788e39ea5e82ae89a28f4
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 23:22:10
Display reorder
380,21,11,1,231,241,220,131,141,151,69,54,59,160,171,176,181,260,270,251,195,205,210,191,309,312,316,102,112,122,27,92,37,42,82,47,87,32,16,6,236,246,156,146,294,64,186,255,275,200,307,310,127,107,97,77,281,226,138,74,166,265,215,314,117,287,297,342,337,347,357,360,352,378,332,371,369,24,14,4,234,244,224,134,144,154,66,51,56,164,174,179,184,264,274,254,199,209,214,194,317,308,313,104,114,124,29,94,39,44,84,49,89,34,19,9,239,249,159,149,291,61,189,259,279,204,315,306,129,109,99,79,284,229,139,70,169,269,219,311,119,289,299,344,339,349,358,364,354,379,334,370,367,22,12,2,232,242,222,132,140,152,68,53,58,162,172,177,182,262,272,252,197,207,212,192,302,304,301,101,110,120,26,90,35,40,81,45,86,31,17,7,237,247,157,147,293,63,187,257,277,202,300,303,125,105,95,76,282,227,135,73,167,267,217,305,115,286,296,341,336,346,355,361,351,377,330,374,365,20,10,0,230,240,221,130,142,150,67,52,57,161,170,175,180,261,271,250,196,206,211,190,319,321,323,100,111,121,25,91,36,41,80,46,85,30,15,5,235,245,155,145,292,62,185,256,276,201,318,320,126,106,96,75,280,225,136,72,165,266,216,322,116,285,295,340,335,345,356,362,350,376,331,372,368,23,13,3,233,243,223,133,143,153,65,50,55,163,173,178,183,263,273,253,198,208,213,193,324,326,328,103,113,123,28,93,38,43,83,48,88,33,18,8,238,248,158,148,290,60,188,258,278,203,329,325,128,108,98,78,283,228,137,71,168,268,218,327,118,288,298,343,338,348,359,363,353,375,333,373,366 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 = {71} 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 23:22:11 · history