Equation 677 Database

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Magma 228c28a9ccde…

magma 228c28a9ccde
Size
336
Isomorphism class hash
228c28a9ccde109b6541866d96ae3793015118b6f5451b566eb117b1f06982af
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 335) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 08:10:15
Display reorder
144,145,146,147,148,149,150,136,137,138,139,140,141,142,143,315,286,254,280,277,203,44,204,176,34,177,205,35,178,206,36,179,207,37,180,208,251,278,287,252,181,198,38,182,199,39,183,200,40,184,201,41,185,202,42,186,284,253,279,285,43,0,20,21,12,13,14,15,16,17,18,19,292,293,294,291,317,326,320,334,302,307,296,297,56,89,57,28,90,29,58,91,30,59,79,31,60,80,32,61,81,33,62,82,22,63,83,23,303,306,295,304,84,24,64,85,25,65,86,26,66,87,27,67,88,209,212,213,214,215,216,217,218,219,230,232,234,210,211,229,323,332,329,327,5,107,100,101,6,108,7,102,263,261,248,264,92,8,109,93,249,265,258,250,110,94,9,111,95,10,112,96,11,113,97,2,103,98,1,104,259,247,262,260,3,105,99,4,106,51,54,55,45,46,47,48,49,50,52,53,299,300,301,298,322,333,324,330,305,310,308,309,68,187,69,121,188,122,70,189,267,255,281,268,71,190,123,72,191,114,73,192,115,74,193,116,256,282,266,257,194,117,75,195,118,76,196,119,77,197,120,78,283,290,288,289,221,222,223,224,225,226,228,231,233,235,220,227,316,325,331,319,128,159,173,174,129,160,130,175,161,164,131,162,165,132,163,166,133,151,167,134,152,168,135,153,274,271,272,275,269,273,276,270,154,169,124,155,170,125,156,171,126,157,172,127,158,237,238,239,240,241,242,243,244,245,246,236,313,314,312,311,321,318,328,335 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 336 = 16 + 5*64, 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#7df1be11e8b03a352a732fe3cebbb8055958b1c7efe44dbc5799cf88069697db, M = {0, 4, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 75} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-08 08:10:16 · history