Equation 677 Database

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Magma 2e124f229bdf…

magma 2e124f229bdf
Size
321
Isomorphism class hash
2e124f229bdfca395d1451ad945b131e5d20d39dc01cd4b9b2563ff2b7846a2a
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 22:28:26
Display reorder
300,124,135,5,154,214,125,136,215,3,155,213,137,123,4,153,120,134,210,0,150,121,132,211,2,151,122,133,212,1,152,205,141,11,130,145,206,142,9,131,146,204,143,10,129,144,140,208,7,126,148,138,209,8,127,149,139,207,6,128,147,306,304,307,309,292,294,110,293,295,296,299,298,108,297,290,291,288,109,289,276,278,279,113,277,280,282,283,111,281,285,286,287,112,284,258,259,116,256,257,263,262,114,260,261,254,255,115,252,253,270,271,119,268,269,274,275,117,272,273,267,266,118,264,265,320,319,318,317,183,46,25,173,202,184,47,203,26,171,201,45,185,24,172,182,42,198,28,169,180,43,199,29,170,181,44,200,27,168,193,37,31,189,179,194,38,32,190,177,192,36,30,191,178,40,196,34,188,175,41,197,35,186,176,39,195,33,187,174,301,303,315,316,82,226,48,63,166,83,227,167,49,64,165,225,81,50,65,78,222,162,51,62,79,223,163,52,60,80,224,164,53,61,157,217,54,73,69,158,218,55,74,70,156,216,56,72,71,220,160,57,76,68,221,161,58,77,66,219,159,59,75,67,305,310,302,308,85,248,107,249,22,86,251,23,105,250,21,246,84,106,247,88,240,18,103,241,89,243,19,104,242,87,245,20,102,244,13,231,98,91,230,14,232,96,92,233,12,229,97,90,228,237,16,101,94,236,239,17,99,95,238,235,15,100,93,234,313,312,311,314 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#41328e14760452489c50b79fcc49c074869181cbfbd0a816da081f28123ef346, 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 22:28:27 · history