Equation 677 Database

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Magma c4320d2786ae…

magma c4320d2786ae
Size
321
Isomorphism class hash
c4320d2786ae40a534d8b3c2c5caf16c70f4e9dcba944410e892a6b5c4a15f7b
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 22:28:22
Display reorder
300,93,84,56,48,75,49,85,91,57,73,86,47,92,55,74,87,89,53,51,77,90,88,54,52,228,229,230,225,50,76,98,82,61,46,70,96,83,62,44,71,97,81,60,45,72,78,94,58,42,69,79,95,59,43,68,80,231,226,224,227,303,315,316,304,285,152,287,284,286,277,150,276,278,279,151,281,280,282,283,148,297,299,296,298,288,149,290,289,291,147,292,294,293,295,265,143,266,264,267,269,141,270,268,271,273,142,274,272,275,146,260,263,261,262,144,252,255,253,254,145,256,258,257,259,320,318,317,319,127,21,165,18,237,220,222,235,163,136,20,17,126,164,137,24,130,168,14,140,128,22,166,15,138,23,129,167,16,139,123,27,160,12,133,124,25,161,10,134,125,26,162,11,135,30,122,159,19,132,28,121,158,13,131,29,234,238,221,236,309,314,310,311,177,66,102,195,194,188,192,178,103,170,67,189,179,104,169,65,176,101,186,172,174,63,99,187,173,64,175,100,185,171,182,210,107,219,218,183,216,108,207,206,184,204,109,213,212,198,181,106,251,250,248,239,232,245,244,242,180,105,201,200,305,301,302,306,117,1,34,193,190,153,191,115,35,8,0,154,116,36,9,3,120,33,157,6,118,4,31,155,7,2,119,32,156,5,112,208,39,217,215,113,214,40,205,203,114,202,41,211,209,196,111,38,249,247,246,233,223,243,240,241,110,37,199,197,308,312,307,313 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#40ac4fa024666665509cd5e942b6a945fc35db692a456c0e176de1fe3e839a09, 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 22:28:23 · history