Equation 677 Database

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Magma 761acca49b5d…

magma 761acca49b5d
Size
321
Isomorphism class hash
761acca49b5db0f607515bde0caf55b00b9c06b1a0135e9ba4039203b67c7340
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 22:21:34
Display reorder
300,24,52,105,81,91,50,25,103,79,89,104,51,80,90,23,107,26,48,216,218,27,106,49,82,242,239,220,211,83,92,40,45,29,76,86,41,43,30,77,87,39,44,28,78,88,75,47,42,31,85,210,209,32,74,84,46,241,240,215,217,304,305,315,307,192,287,284,285,286,279,193,277,276,278,281,283,280,282,191,297,188,299,296,298,189,289,291,288,290,190,293,295,292,294,264,267,198,265,266,268,271,199,269,270,272,275,197,273,274,261,263,260,194,262,255,252,195,253,254,259,257,196,256,258,320,317,318,319,5,166,151,60,233,228,236,246,58,183,150,165,59,184,205,226,1,169,63,187,3,152,167,61,185,4,153,168,62,186,147,34,129,55,180,148,35,130,56,181,149,33,131,57,182,54,37,146,225,232,38,145,128,53,179,36,245,244,212,231,301,316,313,311,137,99,114,70,9,97,135,112,68,10,113,98,69,8,136,117,133,102,73,12,134,115,100,71,13,132,116,101,72,11,110,94,202,214,7,222,95,234,66,206,111,96,201,67,6,65,93,109,251,204,243,221,249,213,237,219,108,138,64,2,303,302,306,308,14,141,124,161,175,139,15,122,159,173,123,140,160,174,16,127,17,144,164,178,18,125,142,162,176,19,126,143,163,177,119,200,20,156,171,120,203,21,157,172,121,235,207,158,230,155,0,224,208,247,250,223,238,227,229,248,118,22,154,170,312,314,310,309 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#101de34e785e3f92e4e627a1da3ddc1fe7ebde0c6c88cd6039e0733ba8ec0ae0, 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 22:21:35 · history