Equation 677 Database

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Magma 510a00312f0f…

magma 510a00312f0f
Size
321
Isomorphism class hash
510a00312f0f4cca06d96dbb833ad309be63e908422ab876a19a93d8963507a1
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 22:55:31
Display reorder
316,258,246,275,236,116,72,14,223,117,71,15,222,73,118,220,16,74,119,221,17,259,247,237,274,70,114,216,12,115,68,13,217,113,69,11,215,67,111,219,9,257,245,235,273,112,66,10,218,48,49,50,51,52,53,46,47,279,277,278,280,306,302,304,318,284,294,282,293,123,205,182,98,124,206,183,99,209,122,102,181,207,120,100,179,121,208,180,101,211,128,96,174,285,295,292,281,129,210,175,97,214,127,95,176,125,212,177,93,126,213,178,94,194,195,193,197,198,196,200,201,202,203,204,199,310,307,300,313,191,5,82,85,192,6,84,83,272,233,251,250,7,190,81,87,234,271,249,252,189,8,86,80,3,184,75,90,185,4,88,76,186,2,89,77,232,270,248,253,187,0,91,78,188,1,92,79,139,140,138,142,143,141,144,145,288,289,290,287,301,319,308,312,291,276,286,283,151,38,107,130,150,39,108,131,242,265,260,256,40,153,132,109,152,41,110,133,42,149,134,106,264,243,255,261,148,43,105,135,44,146,136,103,147,45,104,137,263,244,254,262,58,59,57,54,55,56,64,65,62,60,61,63,303,305,309,311,36,165,20,162,37,166,163,18,35,164,161,19,168,32,23,158,169,33,21,159,34,167,160,22,268,240,239,266,241,269,267,238,28,170,154,24,172,30,27,156,31,173,157,25,29,171,155,26,224,225,226,227,228,229,230,231,298,296,297,299,314,317,315,320 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#cce41c1fd55a940f76617a374756c8d0de5f99032cd8fe3feeb0eb2c48843df6, 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 22:55:32 · history