Equation 677 Database

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Magma 875c49f8dc61…

magma 875c49f8dc61
Size
321
Isomorphism class hash
875c49f8dc6161182ead11a6072b210a88a5be77f5e854be3e5bfa5aa0f9ea04
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 22:27:55
Display reorder
300,152,0,80,28,64,2,153,81,29,65,1,154,79,27,66,77,155,14,205,213,156,78,15,26,241,237,216,206,157,67,17,84,22,172,62,85,18,23,170,63,83,16,21,171,61,20,82,24,168,59,204,217,25,169,60,19,243,238,233,212,304,302,313,315,279,278,176,276,277,282,283,177,280,281,286,287,178,284,285,175,291,290,288,289,295,173,294,292,293,298,174,296,299,297,270,182,269,271,268,183,274,273,275,272,184,266,264,267,265,254,181,253,255,252,258,179,257,259,256,262,180,261,263,260,318,319,317,320,99,138,93,126,223,228,246,245,127,108,139,100,94,128,224,218,101,140,129,109,102,91,141,130,110,142,92,131,103,111,136,86,124,97,106,87,137,125,98,107,88,135,123,96,105,132,89,121,219,221,133,90,122,95,104,134,244,247,220,222,308,310,307,311,188,162,33,53,71,163,189,34,54,72,164,190,35,55,73,32,191,165,56,74,192,30,166,57,75,167,31,58,193,76,160,38,52,235,70,207,161,211,187,215,39,159,51,186,69,158,37,49,234,242,232,239,210,249,214,248,36,50,185,68,305,303,316,314,199,115,9,146,43,116,197,7,147,44,117,198,8,148,45,5,195,118,149,46,196,6,119,150,47,120,4,151,194,48,113,13,144,203,41,11,114,145,201,42,12,227,231,202,209,112,3,229,251,208,225,236,230,250,240,226,10,143,200,40,301,312,306,309 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#3c7860e7d36dbffc79bc7c2d0a8ff0a692ab326401712ae14ddffd4858b8cd98, 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 22:27:56 · history