Equation 677 Database

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Magma dcc540a43c95…

magma dcc540a43c95
Size
321
Isomorphism class hash
dcc540a43c95b8152cb3eb42cdc852943ea92e3283b5fbd2d2bbce895faaddfe
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 22:59:21
Display reorder
300,41,127,111,236,243,39,128,112,234,244,40,113,235,245,126,37,110,130,239,242,38,108,131,237,240,36,109,129,238,241,47,117,125,231,249,232,45,118,123,250,46,119,124,233,251,116,43,121,230,248,114,44,122,228,246,115,42,120,229,247,315,314,301,303,17,264,265,267,266,15,269,268,271,270,16,272,275,274,273,13,260,261,263,262,14,252,253,255,254,12,256,257,259,258,23,289,288,290,291,294,21,293,292,295,22,297,296,298,299,285,19,284,287,286,277,20,276,279,278,281,18,280,283,282,319,317,320,318,53,132,163,179,207,51,133,164,177,208,52,162,178,209,134,49,166,135,175,206,50,167,136,176,204,48,165,137,174,205,59,161,138,170,213,168,57,159,139,214,58,160,140,169,215,157,55,141,173,212,158,56,142,171,210,156,54,143,172,211,307,313,316,304,61,183,33,151,219,62,184,34,152,220,60,35,150,221,185,64,32,182,154,218,65,30,180,155,216,63,31,181,153,217,67,24,189,149,225,147,68,25,190,226,66,26,191,148,227,27,70,188,145,224,28,71,186,146,222,29,69,187,144,223,309,312,305,310,0,84,96,195,72,2,85,97,196,73,1,98,197,74,86,4,99,87,194,75,5,100,88,192,76,3,101,89,193,77,7,102,90,201,78,202,8,103,91,79,6,104,92,203,80,105,10,93,200,81,106,11,94,198,82,107,9,95,199,83,302,311,306,308 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#dcedbe28d6e821630efaff61054e89b4af79513af364c6246d7e9f07a2213221, 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 22:59:22 · history