Equation 677 Database

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Magma f238f025005c…

magma f238f025005c
Size
273
Isomorphism class hash
f238f025005c38abebfcb3c9a899382c37b230974a9aac4fada8e37396698ff2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 272) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 15:54:01
Display reorder
12,13,14,15,16,17,18,19,20,21,22,23,272,97,90,80,98,91,78,96,92,79,100,93,83,101,94,81,99,95,82,103,88,75,104,89,76,102,87,77,106,84,74,107,85,72,105,86,73,119,117,118,115,116,114,110,108,112,113,111,109,263,257,259,271,221,215,201,219,213,202,220,214,203,217,211,200,218,212,198,216,210,199,227,206,192,225,204,193,226,205,194,223,209,195,224,207,196,222,208,197,191,189,190,187,188,186,182,180,184,185,183,181,258,270,269,256,143,173,159,141,171,160,142,172,161,139,169,158,140,170,156,138,168,157,134,179,165,132,177,166,133,178,167,137,175,164,135,176,162,136,174,163,147,148,149,146,144,145,153,154,151,152,150,155,262,264,261,260,232,1,122,233,0,120,231,2,121,228,3,125,229,4,123,230,5,124,238,6,128,239,7,126,237,8,127,234,9,131,235,10,129,236,11,130,248,246,247,251,249,250,243,244,241,242,240,245,266,265,267,268,65,58,45,63,59,46,64,57,47,61,54,44,62,55,42,60,56,43,71,49,36,69,50,37,70,48,38,67,52,39,68,53,40,66,51,41,35,33,34,31,32,30,26,24,28,29,27,25,253,252,254,255 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 273 = 13 + 5*52, 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#3180ad8dfd10ba7152583c35a71774bceecf2852df6e850dd8c0dada693f6036, M = {0, 4, 9, 12, 16, 20, 24, 28, 32, 36, 40, 44, 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, 52): MacNeish's product over GF(4) x GF(13); GF(4) = F_2[x]/(x^2 + 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 2026-10-06 15:54:02 · history