Equation 677 Database

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Magma bb0cb9de9384…

magma bb0cb9de9384
Size
381
Isomorphism class hash
bb0cb9de9384046a5a9df2c2a1db4fec24fe970689a9b4819e8b2ae6f4ceeae7
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 23:50:32
Display reorder
380,163,305,150,176,172,158,168,159,177,154,306,164,151,174,173,156,169,160,178,155,153,162,307,152,175,171,157,170,161,179,142,120,129,146,308,133,128,124,138,137,143,121,130,135,144,309,134,126,125,139,136,122,141,131,145,310,132,127,123,140,149,147,165,166,167,148,347,369,361,360,370,379,378,348,362,350,26,318,13,56,7,18,3,22,9,17,319,24,14,54,8,19,4,23,10,15,16,25,317,12,55,6,20,5,21,11,39,48,29,43,321,30,59,52,38,34,40,49,27,35,44,322,31,57,53,36,33,50,41,28,42,320,32,58,51,37,46,47,1,0,2,45,351,337,335,330,365,336,352,371,353,364,73,312,63,86,82,116,78,69,62,67,313,74,64,84,83,114,79,70,60,68,66,72,311,65,85,81,115,80,71,61,89,98,107,90,315,108,103,99,119,112,87,96,105,113,91,316,109,104,100,117,111,97,88,106,92,314,110,102,101,118,93,94,75,76,77,95,376,355,339,354,331,338,363,366,340,372,211,323,232,224,220,206,216,207,225,238,324,212,233,222,221,204,217,208,226,239,237,210,325,231,223,219,205,218,209,227,193,202,188,197,326,228,184,180,189,236,194,203,186,234,195,327,229,185,181,190,235,201,192,187,196,328,230,183,182,191,200,198,213,214,215,199,332,374,373,333,349,343,377,367,341,342,289,303,265,253,246,278,240,283,260,270,304,290,266,252,249,276,242,284,258,271,272,288,302,264,254,248,277,241,282,259,285,243,263,292,301,267,256,247,281,274,286,244,261,275,293,329,268,257,250,279,273,245,287,262,291,300,269,255,251,280,298,299,295,296,294,297,359,345,368,356,358,344,346,357,334,375 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#f79fc5331f458d02d4e78f64dca968a65056af7ebe34d7d0ef117631414f3151, 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 23:50:33 · history