Equation 677 Database

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Magma 2bc0c6cd5629…

magma 2bc0c6cd5629
Size
321
Isomorphism class hash
2bc0c6cd562925147081372f45dd7ed8981ef033124f17525b90524256d19926
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 22:55:39
Display reorder
300,25,161,177,34,39,35,159,26,175,40,36,160,27,176,41,163,37,28,233,210,162,38,29,178,239,246,209,207,179,42,32,23,182,156,43,33,24,180,157,44,31,22,181,158,45,20,30,184,155,46,206,208,183,154,47,21,238,248,232,211,315,305,311,304,280,283,282,103,281,104,287,284,286,285,102,279,277,278,276,295,106,293,294,292,299,107,296,298,297,291,105,289,290,288,101,272,274,275,273,99,265,266,267,264,100,269,270,271,268,256,97,258,259,257,260,98,262,263,261,252,96,254,255,253,319,318,317,320,115,124,164,60,230,215,244,243,165,143,61,123,114,166,229,223,59,117,167,140,126,57,118,168,141,125,58,116,169,142,64,113,170,122,137,65,111,171,120,138,66,112,172,121,136,109,63,173,222,228,110,62,174,119,139,108,240,247,221,227,306,307,308,309,72,11,87,149,189,147,9,70,88,190,148,10,71,86,188,7,145,68,90,192,8,146,69,91,193,6,144,67,89,191,153,76,93,205,187,231,74,219,13,235,152,75,92,14,186,73,151,95,204,249,216,245,220,236,234,241,150,94,12,185,316,302,301,313,52,199,131,5,79,3,197,53,132,77,4,198,51,130,78,195,0,55,134,82,196,2,56,135,80,194,1,54,133,81,17,50,129,203,84,18,49,128,201,83,19,214,226,202,217,48,16,224,251,218,213,237,225,250,242,212,15,127,200,85,312,303,310,314 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#d283ee665ba0250146cee526d5335dad060ba0eb857bd84eda99570515d555dc, 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 22:55:40 · history