Equation 677 Database

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Magma 673f2b5bf6ba…

magma 673f2b5bf6ba
Size
321
Isomorphism class hash
673f2b5bf6ba5b1cdbb55a1c4dd23327eebe8f2dbc3dba074c40761fbfd95165
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:04:40
Display reorder
300,85,34,120,92,68,93,35,83,121,69,84,36,119,91,67,33,81,122,220,216,32,82,123,95,242,238,218,226,94,70,28,118,2,90,66,29,116,1,88,64,30,117,3,89,65,115,31,4,86,62,225,212,5,87,63,114,236,237,219,215,306,303,301,308,282,193,283,280,281,284,194,286,287,285,278,195,279,277,276,192,294,295,293,292,190,298,299,296,297,191,290,291,289,288,274,275,199,272,273,266,267,200,265,264,270,271,201,269,268,259,258,198,257,256,263,262,196,261,260,255,254,197,253,252,319,320,317,318,186,56,155,140,207,229,240,249,156,13,185,55,154,139,206,214,188,158,142,10,54,189,159,143,11,53,187,157,141,12,184,37,61,14,6,182,38,59,15,7,183,39,60,16,8,40,180,57,208,205,41,181,58,17,9,42,248,241,209,204,310,316,315,312,23,48,76,102,131,103,46,24,77,132,22,47,75,104,130,44,26,79,101,127,45,27,80,99,128,43,25,78,100,129,21,74,52,221,125,211,72,213,96,227,20,73,51,97,124,71,19,50,244,228,243,210,239,222,246,217,18,49,98,126,305,307,302,304,175,107,134,149,164,150,105,176,135,165,174,106,133,148,163,110,178,137,152,167,108,179,138,153,168,109,177,136,151,166,173,202,112,147,162,171,203,111,145,161,172,235,223,146,233,0,170,224,230,247,251,234,245,231,232,250,169,113,144,160,311,313,314,309 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 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#fd865ad85ec1badfd7a7711949755519f1db0e961ea1bdb330ad04fd991385b2, M = {60} 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 2026-10-01 23:04:41 · history