Equation 677 Database

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Magma d1bd40fb9f1f…

magma d1bd40fb9f1f
Size
321
Isomorphism class hash
d1bd40fb9f1fa6ed1793dd95e22cf1142c46bf12c2c99b3cd3f7b744dc3d3f17
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 22:28:33
Display reorder
300,102,2,114,165,179,103,112,163,180,1,101,3,113,164,181,39,104,116,229,232,0,105,115,166,247,237,221,222,167,178,119,42,170,107,173,40,117,168,108,174,41,118,169,106,175,43,120,172,110,176,210,223,171,111,177,109,238,244,230,231,308,309,313,316,281,184,280,283,282,285,284,287,286,182,276,183,277,279,278,187,292,293,295,294,185,297,296,299,298,186,288,289,291,290,272,190,275,273,274,188,265,267,264,266,189,269,271,268,270,193,257,259,256,258,191,261,263,260,262,252,192,253,255,254,318,317,320,319,25,29,69,88,227,208,241,242,148,30,24,31,68,87,226,209,28,71,90,150,32,26,72,91,151,33,27,70,89,149,67,34,86,21,5,35,65,84,22,6,36,66,85,23,7,37,63,82,207,205,38,64,83,19,4,20,236,240,218,204,306,311,305,303,199,140,126,48,58,197,127,49,59,141,198,139,128,50,57,136,195,129,51,54,137,196,130,52,55,138,194,131,53,56,124,133,47,235,62,224,125,212,203,214,132,123,46,200,61,135,121,44,233,239,225,245,211,250,213,248,134,122,45,60,314,302,315,301,158,18,143,77,96,159,144,78,97,16,157,17,142,76,95,14,161,146,80,99,15,162,147,81,100,13,160,145,79,98,152,10,75,202,94,8,153,74,156,93,9,228,217,201,220,12,155,215,251,219,206,246,216,249,243,234,11,154,73,92,304,307,312,310 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#47b26c2e0558f6c4fdff38c956d09d23d3aef780160b6fe0856dd3e8f07caf34, 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 22:28:34 · history