Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 36adea7beb41…

magma 36adea7beb41
Size
381
Isomorphism class hash
36adea7beb4167dd7532554b87beefe9f8e5075931b9338b55509dfa7b9f511c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:19:11
Display reorder
380,87,82,62,67,72,77,237,212,217,222,227,232,282,287,292,297,272,277,22,27,2,7,12,17,152,157,162,167,172,177,42,47,52,57,32,37,127,132,137,142,147,122,180,185,190,195,201,207,97,102,107,112,117,92,315,316,317,312,313,314,242,267,247,252,257,262,362,336,372,343,368,345,334,350,377,358,88,83,64,69,73,78,239,214,218,223,228,234,283,288,293,298,274,279,24,29,4,9,14,19,153,158,164,168,173,178,44,49,54,59,34,39,129,134,139,144,148,123,183,189,194,199,204,208,99,104,109,114,118,93,305,301,300,302,303,304,243,269,248,253,259,264,363,348,373,333,367,344,341,353,378,357,86,81,60,65,70,75,235,211,216,221,226,231,280,286,291,296,270,275,21,26,0,5,11,16,151,156,161,166,171,175,40,45,51,56,30,35,125,130,135,141,146,120,182,187,192,197,200,206,95,100,105,111,116,90,320,321,322,323,318,319,241,266,246,251,256,261,360,332,371,347,366,340,331,351,376,355,89,84,63,68,74,79,238,213,219,224,229,233,284,289,294,299,273,278,23,28,3,8,13,18,154,159,163,169,174,179,43,48,53,58,33,38,128,133,138,143,149,124,184,188,193,198,203,209,98,103,108,113,119,94,324,325,326,327,328,329,244,268,249,254,258,263,364,349,374,338,369,342,335,354,379,359,85,80,61,66,71,76,236,210,215,220,225,230,281,285,290,295,271,276,20,25,1,6,10,15,150,155,160,165,170,176,41,46,50,55,31,36,126,131,136,140,145,121,181,186,191,196,202,205,96,101,106,110,115,91,310,311,306,307,308,309,240,265,245,250,255,260,361,346,370,330,365,339,337,352,375,356 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, M = {70} 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, 76): MacNeish's product over GF(4) x GF(19); 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:19:12 · history