Equation 677 Database

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Magma 5c11bc1b2709…

magma 5c11bc1b2709
Size
321
Isomorphism class hash
5c11bc1b270976d05b5866aea72f8e273a88374b03dd562695a9decd4c338501
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 22:37:12
Display reorder
300,198,112,147,183,143,199,141,113,148,184,111,142,200,149,185,201,108,139,146,182,202,109,140,144,180,203,110,138,145,181,118,134,153,196,189,132,119,154,197,190,195,133,117,155,191,114,137,152,192,188,115,135,150,193,186,116,136,151,194,187,315,316,304,303,265,90,267,266,264,269,268,91,271,270,92,273,272,275,274,261,93,260,263,262,253,94,252,255,254,257,95,256,259,258,88,289,290,288,291,293,89,294,292,295,297,296,87,299,298,84,284,286,285,287,85,277,278,276,279,86,280,282,281,283,320,319,318,317,234,70,207,39,235,236,237,71,208,40,69,239,238,209,41,232,66,233,206,38,229,67,228,204,36,231,68,230,205,37,61,246,213,247,45,248,62,214,249,46,251,250,60,215,47,64,244,212,245,44,65,240,210,241,42,63,242,211,243,43,310,309,307,308,159,7,53,219,76,160,77,8,51,220,6,75,161,52,221,158,10,72,49,218,156,11,73,50,216,157,9,74,48,217,5,82,59,165,225,83,3,57,166,226,167,81,4,58,227,0,78,55,164,224,2,79,56,162,222,1,80,54,163,223,311,312,306,301,18,177,25,123,97,19,98,178,26,124,179,96,20,24,125,21,176,100,28,122,22,174,101,29,120,23,175,99,27,121,168,103,31,16,129,104,169,32,17,130,15,102,170,30,131,171,106,34,12,128,172,107,35,13,126,173,105,33,14,127,314,313,302,305 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#69e303b0df9a949f679bcb1932ca3e0d44707fb71c41006ed01ea0a3f8179ab7, 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 22:37:18 · history